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                                 UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM N-Q

                   CERTIFIED SHAREHOLDER REPORT OF REGISTERED
                        MANAGEMENT INVESTMENT COMPANIES



		Investment Company Act file number 811-21321


                          Pioneer Municipal High Income Trust
               (Exact name of registrant as specified in charter)


                       60 State Street, Boston, MA 02109
              (Address of principal executive offices) (ZIP code)


            Dorothy E. Bourassa, Pioneer Investment Management, Inc.,
                       60 State Street, Boston, MA 02109
                    (Name and address of agent for service)


Registrant's telephone number, including area code:  (617) 742-7825


Date of fiscal year end:  April 30


Date of reporting period:  July 31, 2004


Form N-Q is to be used by management investment companies, other than small
business investment companies registered on Form N-5 (239.24 and 274.5 of this
chapter), to file reports with the Commission, not later than 60 days after
close of the first and third fiscal quarters, pursuant to Rule 30b1-5under
the Investment Company Act of 1940 (17 CFR 270.30b-5).  The Commission may
use the information provided on Form N-Q in its regulatory, disclosure review,
inspection, and policymaking roles.

A registrant is required to disclose the information specified by Form N-Q,
and the Commission will make this information public. A registrant is not
required to respond to the collection of information contained in Form N-Q
unless the Form displays a currently valid Office of Management and Budget
("OMB") control number. Please direct comments concerning the accuracy of the
information collection burden estimate and any suggestions for reducing the
burden to Secretary, Securities and Exchange Commission, 450 Fifth Street, NW,
Washington, DC 20549-0609.  The OMB has reviewed this collection of information
under the clearance requirements of 44 U.S.C. ss. 3507.



ITEM 1. Schedule of Investments.

			                      


Pioneer Municipal High Income Trust

SCHEDULE OF INVESTMENTS 7/31/04 (unaudited)



Principal    S&P/Moody's
Amount       Ratings                                                                                         Value
                          TAX EXEMPT OBLIGATIONS  - 127.6% OF NET ASSETS
                          Alabama - 3.6%
 $ 10,000,000AAA/Aaa      Birmingham Alabama General Obligation, 5.0%, 12/1/32                        $        10,000,700
      1,500,0BBB/NR       Camden Alabama Industrial Development Board, 6.125%, 12/1/24                    1,565,940
                                                                                                      $   11,566,640
                          Arizona - 6.0%
      5,000,0B+/Ba3       Apache County Industrial Development Authority, 5.85%, 3/1/28               $          4,862,700
      5,000,0B+/Ba3       Apache County Industrial Development Authority, 5.875%, 3/1/33                  4,835,250
      3,000,0NR/NR        Maricopa County Industrial Development Authority, 7.875%, 4/1/27                3,072,690
      5,880,0AA/Aa2       Salt River Project Agriculture Improvement and Power District Electric
                             System Revenue, 5.0%, 1/1/31                                                 5,895,758
         500,NR/Baa2      Yavapai County Industrial Development Authority, 6.0%, 8/1/33                     504,495
                                                                                                      $   19,170,893
                          California - 10.9%
      7,270,0BBB/A3       California State General Obligation, 5.25%, 2/1/28                          $          7,330,196
      5,150,0BBB/Baa3     Golden State Tobacco Securitization Corp., 7.8%, 6/1/42                                5,227,816
      7,000,0BBB/Baa3     Golden State Tobacco Securitization Corp., 7.875%, 6/1/42                       7,139,160
      4,000,0AAA/Aaa      Palm Desert Financing Authority Tax Allocation Revenue, 5.0%, 4/1/30            3,988,240
      3,000,0AAA/Aaa      San Diego Unified School District, 5.0%, 7/1/25                                 3,028,950
      2,500,0AAA/Aaa      University of California Revenue, 5.0%, 5/15/25                                 2,533,550
      7,000,0B+/NR        Valley Health System Hospital Revenue, 6.5%, 5/15/25                            5,874,750
                                                                                                      $   35,122,662
                          Connecticut - 1.6%
      2,205,0BB/Ba1       Connecticut State Health & Educational Facilities Authority Revenue, 5.375%,$    1,838,264
      4,400,0BB/Ba1       Connecticut State Health & Educational Facilities Authority Revenue, 5.5%, 7/1   3,391,388
                                                                                                      $    5,229,652
                          District of Columbia - 3.4%
      5,000,0BBB/Baa3     District of Columbia Tobacco Settlement Financing Corp., 6.5%, 5/15/33      $    4,334,200
      7,325,0BBB/Baa3     District of Columbia Tobacco Settlement Financing Corp., 6.75%, 5/15/40          6,480,647
                                                                                                      $   10,814,847
                          Florida - 4.5%
      2,000,0NR/NR        Beacon Lakes Community Development, 6.9%, 5/1/35                            $    2,074,380
      2,300,0CCC-/Caa3    Hillsborough County Aviation Authority Revenue, 6.8%, 1/1/24                     1,115,638
      1,650,0BBB-/Baa2    Polk County Industrial Development Revenue, 5.85%, 12/1/30                       1,631,058
      2,000,0NR/NR        Seminole Tribe Convention-A, 8.95%, 10/1/33                                      2,309,480
      1,900,0NR/NR        Seminole Tribe Convention-A, 10.0%, 10/1/33                                      2,263,527
      5,000,0NR/Baa2      Tallahassee Health Facilities Revenue, 6.375%, 12/1/30                           5,020,100
                                                                                                      $   14,414,183
                          Idaho - 1.6%
      5,000,0BB+/Ba3      Power County Industrial Development Corp., 6.45%, 8/1/32                    $    5,101,650

                          Illinois - 3.9%
      1,000,0NR/NR        Centerpoint Intermodal Center, 8.0%, 6/15/23 (144A)                         $      971,310
      2,790,0CCC-/Ca      Chicago Illinois O'Hare International Airport, 6.45%, 5/1/18                     1,129,950
      1,500,0NR/NR        Illinois Health Facilities Authority Revenue, 6.9%, 11/15/33                     1,477,545
    16,880,(aAAA/Aaa      Metropolitan Pier & Exposition Authority Dedicated State Tax Revenue,
                             0.0%, 6/15/22                                                                 9,091,399
                                                                                                      $   12,670,204
                          Indiana - 1.1%
 4,300,000   CCC/Caa3     Indiana State Development Finance Authority Revenue, 5.75%, 10/1/11         $    3,585,254




Pioneer Municipal High Income Trust

SCHEDULE OF INVESTMENTS 7/31/04 (unaudited) (continued)


Principal    S&P/Moody's
Amount       Ratings                                                                                         Value
                          Kentucky - 2.2%
 $   7,050,00CCC-/Caa2    Kenton County Airport Revenue, 7.5%, 2/1/12                                 $    5,693,369
 1,965,000   CCC-/Caa2    Kenton County Airport Revenue, 7.5%, 2/1/20                                      1,491,690
                                                                                                      $    7,185,059
                          Massachusetts - 8.4%
 2,435,000   AAA/Aaa      Massachusetts Health & Educational Facilities Authority Revenue, 5.0%, 7/15/$    2,437,070
 7,050,000   AAA/Aaa      Massachusetts Health & Educational Facilities Authority Revenue, 5.125%, 7/15/   7,074,534
 1,000,000   AA/NR        Massachusetts Health & Educational Facilities Authority Revenue, 5.25%, 10/15/   1,008,570
 2,640,000   BBB/Baa3     Massachusetts Health & Educational Facilities Authority Revenue, 5.75%, 7/1/28   2,566,397
 3,500,000   BBB/Baa3     Massachusetts Health & Educational Facilities Authority Revenue, 6.25%, 7/1/22   3,615,640
 5,000,000   BBB-/NR      Massachusetts Health & Educational Facilities Authority Revenue, 6.75%, 10/1/3   5,105,500
    75,000   BB/NR        Massachusetts State Development Finance Agency, 5.25%, 10/1/18                      64,464
 5,055,000   AA-/Aa3      Massachusetts State Housing Finance Agency, 5.25%, 12/1/33                       4,987,566
                                                                                                      $   26,859,741
                          Michigan - 4.3%
 1,500,000   BBB-/NR      John Tolfree Health System Corp., 6.0%, 9/15/23                             $    1,424,400
 4,010,000   BBB-/Baa3    Michigan State Hospital Finance Authority Revenue, 6.0%, 2/1/24                  3,841,740
 2,000,000   NR/NR        Michigan State Hospital Finance Authority Revenue, 6.4%, 1/1/15                  1,944,300
 7,690,000   NR/NR        Wayne Charter County Special Airport Facilities Revenue, 6.75%, 12/1/15          6,552,572
                                                                                                      $   13,763,012
                          Minnesota - 3.9%
13,260,000   NR/NR        Minneapolis/St. Paul Metropolitan Airports, 7.0%, 4/1/25                    $   11,035,502
 1,500,000   BB/Ba2       St. Paul Housing & Redevelopment Authority, 6.625%, 11/1/17                      1,514,520
                                                                                                      $   12,550,022
                          Mississippi - 0.9%
 3,000,000   BBB-/Ba1     Mississippi Business Finance Corp. Pollution Control Revenue, 5.9%, 5/1/22  $    3,024,210

                          Missouri - 1.5%
 5,500,000   NR/Ba3       St. Louis Industrial Development Authority Revenue, 7.25%, 12/15/35         $    4,825,975

                          Nevada - 1.4%
 1,000,000   BBB-/Baa2    Clark County Industrial Development Revenue, 5.45%, 3/1/38                  $    1,041,680
 1,850,000   B-/NR        Clark County Industrial Development Revenue, 5.5%, 10/1/30                       1,581,768
 2,000,000   NR/NR        Nevada State Department of Business & Industry, 7.25%, 1/1/23                    1,970,900
                                                                                                      $    4,594,348
                          New Hampshire - 0.9%
 3,000,000   AAA/Aaa      Manchester School Facilities Revenue, 5.125%, 6/1/28                        $    3,050,550

                          New Jersey - 8.0%
 2,000,000   B/Caa2       New Jersey Economic Development Authority Revenue, 6.25%, 9/15/19           $    1,584,780
11,700,000   B/Caa2       New Jersey Economic Development Authority Revenue, 6.25%, 9/15/29                8,744,346
 1,000,000   B/Caa2       New Jersey Economic Development Authority Revenue, 6.4%, 9/15/23                   783,510
 6,150,000   B/Caa2       New Jersey Economic Development Authority Revenue, 7.0%, 11/15/30                4,816,373
10,750,000   BBB/Baa3     Tobacco Settlement Financing Corp., 6.75%, 6/1/39                                9,683,600
                                                                                                      $   25,612,609
                          New Mexico - 1.3%
 3,700,000   NR/NR        New Mexico Hospital Equipment Loan Council, 6.4%, 6/1/16                    $    4,042,953

                          New York - 5.8%
 2,000,000   A/NR         New York City Industrial Development Agency, 5.375%, 6/1/23                 $    1,998,660
 5,625,000   CCC/Caa2     New York City Industrial Development Agency, 6.9%, 8/1/24                        3,503,194
 5,000,000   AAA/Aaa      New York City Trust Cultural Resources Revenue, 5.125%, 7/1/31                   5,059,800
 2,000,000   NR/NR        Suffolk County Industrial Development Agency, 7.25%, 1/1/30                      1,872,700
 6,000,000   AAA/Aaa      Triborough Bridge & Tunnel Authority Revenue, 5.25%, 11/15/30                    6,154,800
                                                                                                      $   18,589,154
                          North Carolina - 1.4%
 2,000,000   AA+/Aa2      Charlotte North Carolina Certificates of Participation, 5.0%, 6/1/33        $    1,981,760
 4,600,000   NR/NR        Charlotte North Carolina Special Facilities Revenue, 7.75%, 2/1/28               2,415,000
                                                                                                      $    4,396,760


Pioneer Municipal High Income Trust

SCHEDULE OF INVESTMENTS 7/31/04 (unaudited) (continued)


Principal    S&P/Moody's
Amount       Ratings                                                                                         Value
                          Oklahoma - 4.9%
 $   3,000,00B-/B1        Oklahoma Development Finance Authority Revenue, 5.625%, 8/15/19             $    3,029,940
 8,000,000   B-/B1        Oklahoma Development Finance Authority Revenue, 5.625%, 8/15/29                  8,079,840
 4,100,000   B-/Caa2      Tulsa Municipal Airport Revenue, 5.65%, 12/1/35                                  3,730,877
 1,225,000   B-/Caa2      Tulsa Municipal Airport Revenue, 6.25%, 6/1/20                                     916,729
                                                                                                      $   15,757,386
                          Oregon - 4.8%
 1,000,000   NR/NR        Klamath Falls Electric Revenue, 5.75%, 1/1/13                               $    1,001,960
 7,000,000   NR/NR        Klamath Falls Electric Revenue, 6.0%, 1/1/25                                     6,764,030
 7,500,000   NR/NR        Western Generation Agency Cogeneration Project Revenue, 7.125%, 1/1/21           7,583,400
                                                                                                      $   15,349,390
                          Pennsylvania - 10.9%
 1,550,000   NR/Baa1      Allegheny County Hospital Development Authority Revenue, 5.125%, 5/1/25     $    1,326,180
12,300,000   B/B2         Allegheny County Hospital Development Authority Revenue, 9.25%, 11/15/30        13,782,150
 2,500,000   BBB-/Baa2    Beaver County Industrial Development Authority, 7.625%, 5/1/25                   2,642,900
 1,000,000   BB-/NR       Columbia County Hospital Authority Health Care Revenue, 5.9%, 6/1/29               786,270
 5,000,000   BBB/Baa3     Delaware County Industrial Development Authority Revenue,  6.1%, 7/1/13          5,260,600
 1,280,000   NR/B2        Langhorne Manor Borough Higher Education & Health Authority Revenue, 7.35%, 7/   1,235,520
 2,500,000   BBB+/NR      Pennsylvania Higher Educational Facilities Authority Revenue, 5.4%, 7/15/36      2,459,550
 2,230,000   AAA/Aaa      Pennsylvania State Turnpike Commission, 5.0%, 7/15/10                            2,435,517
 5,000,000   BBB-/Baa2    Philadelphia Hospitals & Higher Education Facilities Authority Revenue, 6.5%,    5,000,300
                                                                                                      $   34,928,987
                          South Carolina - 8.7%
 4,250,000   BBB/Baa2     Georgetown County Environmental Improvement Revenue, 5.95%, 3/15/14         $    4,623,958
15,000,000   AA-/A1       Greenville County School District, 5.5%, 12/1/28                                15,285,450
 1,900,000   BBB/Baa2     South Carolina Jobs Economic Development Authority Revenue, 6.25%, 8/1/31        1,955,290
 5,850,000   BBB/Baa2     South Carolina Jobs Economic Development Authority Revenue, 6.375%, 8/1/34       6,069,609
                                                                                                      $   27,934,307
                          Tennessee  - 5.2%
 7,000,000   BBB+/Baa2    Johnson City Health & Educational Facilities Board Hospital Revenue, 7.5%, 7$    8,084,230
 4,480,000   NR/Baa2      Knox County Health Educational & Housing Facilities Board Hospital Revenue, 6.   4,231,046
 4,055,000   BBB/Baa2     Memphis-Shelby County Airport Authority Special Facilities Revenue, 5.05%, 9/1   4,236,218
                                                                                                      $   16,551,494
                          Texas  - 7.7%
 6,500,000   CCC/Caa2     Alliance Airport Authority Special Facilities Revenue, 7.0%, 12/1/11        $    5,379,140
 7,500,000   CCC/Caa2     Alliance Airport Authority Special Facilities Revenue, 7.5%, 12/1/29             5,137,275
 1,345,000   NR/Baa3      Bexar County Housing Finance Corp., 8.0%, 12/1/36                                1,395,747
 5,500,000   CCC-/Caa2    Dallas-Fort Worth International Airport Revenue, 7.125%, 11/1/26                 2,307,470
 2,800,000   CCC-/Caa2    Dallas-Fort Worth International Airport Revenue, 7.6%, 11/1/11                   1,378,496
   750,000   CCC-/Caa2    Dallas-Fort Worth International Airport Revenue, 7.625%, 11/1/21                   328,133
 1,000,000   BB/NR        Georgetown Health Facilities Development Corp., 6.25%, 8/15/29                     939,250
 3,750,000   B-/Caa2      Houston Airport System Special Facilities Revenue, 5.7%, 7/15/29                 2,490,113
 5,000,000   BBB/NR       Lufkin Health Facilities Development Corp. 5.7%, 2/15/28                         4,704,150
   500,000   BBB/Baa2     Sabine River Authority Pollution Control Revenue, 6.15%, 8/1/22                    518,515
                                                                                                      $   24,578,289
                          Vermont  - 0.5%
 1,500,000   A-/A3        Vermont Educational & Health Buildings Financing Agency Revenue, 6.0%, 10/1/$    1,629,360

                          Virginia  - 1.4%
 1,000,000   BBB/Baa3     Peninsula Ports Authority, 6.0%, 4/1/33                                     $    1,026,080
 4,000,000   BB/NR        Pocahontas Parkway Association of Virginia Toll Road Revenue, 5.5%, 8/15/28      3,355,320
                                                                                                      $    4,381,400
                          Washington - 5.3%
 4,710,000   AAA/Aaa      Spokane Public Facilities District Hotel/Motel Tax & Sales, 5.75%, 12/1/27  $    5,112,564
 7,025,000   BBB/Baa3     Tobacco Settlement Authority Washington, 6.625%, 6/1/32                          6,199,211
14,315,000   AAA/Aaa      Washington State General Obligation, 0.0%, 6/1/22                                5,621,357
                                                                                                      $   16,933,132


Pioneer Municipal High Income Trust

SCHEDULE OF INVESTMENTS 7/31/04 (unaudited) (continued)


Principal    S&P/Moody's
Amount       Ratings                                                                                         Value
                          Wyoming - 1.6%
 $   5,000,00BB+/Ba3      Sweetwater County Solid Waste Disposal Revenue, 6.9%, 9/1/24                $    5,081,750

                          TOTAL TAX-EXEMPT OBLIGATIONS
                          (Cost $405,609,905)                                                         $  409,295,873

  Shares                  TAX-EXEMPT MONEY MARKET MUTUAL FUND - 1.1% OF NET ASSETS
 3,452,361                BlackRock Provident Institutional Municipal Fund                            $    3,452,361
                          TOTAL TAX-EXEMPT MONEY MARKET MUTUAL FUND
                          (Cost $3,452,361)                                                           $    3,452,361

                          TOTAL INVESTMENTS IN SECURITIES - 128.7%
                          (Cost $409,062,266) (b) (c) (d)                                             $  412,748,234
                          Other Assets in Excess of Liabilities -  2.8%                               $    9,023,328
                          Preferred Shares at Redemption Value - (31.5)%                             $  -101,000,000
                          NET ASSETS APPLICABLE TO COMMON SHAREOWNERS - 100.0%                        $  320,771,562

       NR:   Security not rated by S&P or Moody's.

    (144A)   Security is exempt from registration under Rule 144A of the Securities Act of 1933.  Such
             securities may be resold normally to qualified institutional buyers in a transaction exempt
             from registration.  At July 31, 2004 the value of these securities amounted to
             $971,310 or 0.3% of net assets applicable to common shareholders.

       (a)   Indicates a security that has a zero coupon that remains in effect until a predetermined date at which time the
             stated coupon rate becomes effective until final maturity.

       (b)   The concentration of investments by type of obligation/market sector is as follows:
             Insured                                                                                            16.1%
             General Obligation                                                                                  1.8
             Revenue Bonds:
                                 Health Revenue                                                                 25.0
                                 Airport Revenue                                                                18.1
                                 Tobacco Revenue                                                                 9.5
                                 Education Revenue                                                               7.0
                                 Pollution Control Revenue                                                       6.9
                                 Power Revenue                                                                   5.4
                                 Development Revenue                                                             3.3
                                 Other                                                                           1.9
                                 Facilities Revenue                                                              1.6
                                 Housing Revenue                                                                 1.6
                                 Transportation Revenue                                                          1.5
                                 Utilities Revenue                                                               0.3
                                                                                                               100.0%

       (c)   At July 31, 2004, the net unrealized gain on investments based on cost for federal income tax purposes
             of $408,488,776 was as follows:

             Aggregate gross unrealized gain for all investments in which
             there is an excess of value over tax cost                                                $  $    17,052,661

             Aggregate gross unrealized loss for all investments in which
             there is an excess of tax cost over value                                                   -12,793,202
             Net unrealized gain                                                                      $  $      4,259,459

             For financial reporting purposses net unrealized gain on investments was $3,685,968
             and cost of investments aggregated $409,062,266












ITEM 2. CONTROLS AND PROCEDURES.

(a) Disclose the conclusions of the registrant's principal executive officer or
officers and principal financial officer or officers, or persons performing
similar functions, about the effectiveness of the registrant's disclosure
controls and procedures (as defined in Rule 30a-3(c) under the Act (17 CFR
270.30a-3(c))) as of a date within 90 days of the filing date of the report
that includes the disclosure required by this paragraph, based on their
evaluation of these controls and procedures required by Rule 30a-3(b)
under the Act (17 CFR270.30a-3(b))) and Rule 13a-15(b) or 15d-15(b)
under the Exchange Act (17 CFR240.13a-15(b) or 240.15d-15(b)).

The registrant's certifying officers have determined that the registrant's
disclosure controls and procedures are effective based on an evaluation of
these controls and procedures as of a date within 90 days prior to the filing
date of this report.

(b) Disclose any change in the registrant's internal controls over financial
reporting (as defined in Rule 30a-3(d) under the Act (17 CFR270.30a-3(d))
that occurred during the registrant's last fiscal quarter that has materially
affected, or is reasonably likely to materially affect, the registrant's
internal control over financial reporting.

There were no significant changes in the registrant's internal controls over
financial reporting that occurred during the registrant's last fiscal quarter
that have materially affected, or is reasonably likely to materially affect,
the registrant's internal control over financial reporting.



ITEM 3. EXHIBITS.

(a) A separate certification for each principal executive officer and principal
financial officer of the registrant as required by Rule 30a-2 under the Act
(17 CFR 270.30a-2).

Filed herewith.






                                   SIGNATURES

                          [See General Instruction F]


Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, the registrant has duly caused this report to be
signed on its behalf by the undersigned, thereunto duly authorized.


(Registrant) Pioneer Municipal High Income Trust


By (Signature and Title)* /s/ John F. Cogan, Jr.
John F. Cogan, Jr, President

Date September 28, 2004


Pursuant to the requirements of the Securities Exchange Act of 1934 and the
Investment Company Act of 1940, this report has been signed below by the
following persons on behalf of the registrant and in the capacities and on the
dates indicated.


By (Signature and Title)* /s/ John F. Cogan, Jr.
John F. Cogan, Jr., President

Date September 28, 2004


By (Signature and Title)* /s/ Vincent Nave
Vincent Nave, Treasurer

Date September 28, 2004

* Print the name and title of each signing officer under his or her signature.