<PAGE>   1
                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 10-Q

                  QUARTERLY REPORT UNDER SECTION 13 OR 15(d) OF
                       THE SECURITIES EXCHANGE ACT OF 1934



FOR THE QUARTER ENDED JUNE 30, 1998  COMMISSION FILE NUMBER 2-22997



                                MILLS MUSIC TRUST
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)



           NEW YORK                                 13-6183792
(STATE OR OTHER JURISDICTION OF                  (I.R.S. EMPLOYER
 INCORPORATION OR ORGANIZATION)                 IDENTIFICATION NO.)



C/O MARINE MIDLAND BANK,   140 BROADWAY,   NEW YORK, NY       10015
   (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)                (ZIP CODE)



REGISTRANT'S TELEPHONE NUMBER, INCLUDING AREA CODE    (212) 658-6014



               INDICATE BY CHECK-MARK WHETHER THE REGISTRANT (1) HAS FILED ALL
REPORTS REQUIRED TO BE FILED BY SECTION 13 OR 15(D) OF THE SECURITIES EXCHANGE
ACT OF 1934 DURING THE PRECEDING 12 MONTHS (OR FOR SUCH SHORTER PERIOD THAT THE
REGISTRANT WAS REQUIRED TO FILE SUCH REPORTS), AND (2) HAS BEEN SUBJECT TO SUCH
FILING REQUIREMENTS FOR THE PAST 90 DAYS.


                                    YES X      NO


NUMBER OF TRUST UNITS OUTSTANDING AS OF MARCH 10, 1998    277,712
<PAGE>   2
                                                                          Page 2



                          PART I - FINANCIAL STATEMENTS

Item 1.  Financial Information

                                MILLS MUSIC TRUST
                  STATEMENTS OF CASH RECEIPTS AND DISBURSEMENTS
            THREE MONTHS AND SIX MONTHS ENDED JUNE 30, 1998 AND 1997

                                   (UNAUDITED)





<TABLE>
<CAPTION>
                                                                   Three Month Ended                      Six Months Ended
                                                                       June 30,                             June 30,
                                                             1998                 1997                1998               1997
                                                             ----                 ----                ----               ----
<S>                                                       <C>                  <C>                 <C>                <C>
Receipts:
      Mills Music, Inc.                                    $273,049             $227,996            $472,931           $487,169

Undistributed cash
at beginning of the period                                        0                   13                   8                 20

Disbursements -
administrative expenses                                     ( 7,600)            ( 14,213)           ( 19,871)           (25,063)
                                                             ------              -------             -------             ------

Balance available for distribution                          265,449              213,796             453,068            462,126

Cash distribution to unit holders                           265,438              213,783             453,057            462,113
                                                            -------              -------             -------            -------

Undistributed cash at end of the period                    $    11              $     13            $     11           $     13
                                                           =======             =========            ========           ========

Cash distribution per
unit (based on 277,712 units outstanding)                  $   .95              $    .77            $   1.63           $   1.66
                                                           =======              ========            ========           ========
</TABLE>

See accompanying Notes to Statements of Cash Receipts and Disbursements.
<PAGE>   3
                                                                          Page 3


                                MILLS MUSIC TRUST
             NOTES TO STATEMENTS OF CASH RECEIPTS AND DISBURSEMENTS
            THREE MONTHS AND SIX MONTHS ENDED JUNE 30, 1998 AND 1997

                                   (UNAUDITED)

NOTE 1.  ACCOUNTING POLICIES AND GENERAL INFORMATION

                      Mills Music Trust ("the Trust") was created in 1964 for
         the purpose of acquiring the rights to receive payments of a deferred
         contingent purchase price contract obligation payable by Mills Music,
         Inc. ("Mills"). The contingent payments are determined quarterly, and
         are based on a formula which takes into account gross royalty income
         from certain music copyrights and licenses of Mills, less royalties
         paid and amounts deducted by Mills in accordance with contract terms.

                      Payments from Mills to the Trust are made in March, June,
         September, and December, and include net royalty income of the
         preceding calendar quarter. The payments received are accounted for on
         a cash basis, as are expenses paid. The Declaration of Trust requires
         the distribution of all funds received by the Trust to the Unit holders
         after payment of expenses.

                      The statements of cash receipts and disbursements reflect
         only cash transactions and do not present transactions that would be
         included in financial statements presented on the accrual basis of
         accounting, as contemplated by generally accepted accounting
         principles.

                      There is no book value per unit because cumulative
         distributions are in excess of the initial investment in the Trust.

NOTE 2.  RELATED PARTY TRANSACTIONS

                      The Declaration of Trust provides that each trustee shall
         receive reimbursement for expenses reasonably incurred in the
         performance of his duties and annual compensation of $2,500 per year
         for his services as trustee, provided that such aggregate compensation
         to the trustees as a group may not exceed 3% of the monies received by
         the Trust in any year. The Declaration of Trust further provides for
         reimbursement to the corporate trustee for its clerical and
         administrative services to the Trust. Accordingly, Marine Midland Bank
         receives reimbursement for such services and for services performed as
         Registrar and Transfer Agent. The Declaration of Trust further provides
         that if any trustee performs unusual or extraordinary services,
         reasonable compensation for such services shall be paid, subject to
         certain
<PAGE>   4
                                                                          Page 4



                                MILLS MUSIC TRUST
             NOTES TO STATEMENTS OF CASH RECEIPTS AND DISBURSEMENTS
            THREE MONTHS AND SIX MONTHS ENDED JUNE 30, 1998 AND 1997
                                   (CONTINUED)

                                   (UNAUDITED)

               limitations and to prior confirmation by a majority in interest
               of Trust Certificate holders. Pursuant to these provisions,
               disbursements to related parties were made as follows for the six
               months ended June 30, 1998 and 1997.

<TABLE>
<CAPTION>
                                                      1998            1997
                                                      ----            ----
<S>                                                  <C>             <C>
               Trustee Fees:
                 Bernard D. Fischman                 $1,250          $1,250
                 Marine Midland Bank                  1,250           1,250

               Marine Midland Bank - Transfer
                 Agent and Registrar                      0           5,932
</TABLE>

NOTE 3.  ROYALTY EXAMINATION

                      The Trust's claim against Belwin Mills Publishing
         Corporation, the former administrators of the Old Mills Catalogue, in
         connection with a 1987 royalty examination is pending final resolution
         by the Trust. It cannot be determined at this time, what, if any,
         amount may ultimately be received by the Trust. No examination of
         royalty information has been performed subsequent to 1987.


NOTE 4.  FEDERAL INCOME TAXES

                      No provision for income taxes has been made since the
         liability is that of the unit holders and not the Trust.
<PAGE>   5
                                                                          Page 5


                          PART I - FINANCIAL STATEMENTS


Item 2.  Management's Discussion and Analysis of Results of Operations

                      The Trust's receipts from Mills Music, Inc. are derived
         from copyrights established prior to 1964 and such receipts fluctuate
         based upon public interest in the "nostalgia" appeal of older songs.



                           PART II - OTHER INFORMATION

                      Items 1 through 6, inclusive, are not applicable.
<PAGE>   6
                                                                          Page 6



                                   SIGNATURES


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


                                               MILLS MUSIC TRUST
                                          ---------------------------
                                                 (Registrant)





Date     July 21, 1998                 By:     BERNARD D. FISCHMAN
         -------------                     -------------------------------------
                                           Bernard D. Fischman,Trustee




Date     July 21, 1998                 By:      MARCIA MARKOWSKI
         -------------                     -------------------------------------
                                           Marine Midland Bank
                                           Corporate Trustee