<PAGE>   1
                                    FORM 10-Q


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

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

                      For the quarter ended March 31, 2000

                           Commission File No. 0-10810

                              KIEWIT ROYALTY TRUST
             (Exact name of Registrant as specified in its charter)

<TABLE>
<S>                                           <C>
           Nebraska                                 47-6131402
-------------------------------                 -----------------------------------------------
(State or other jurisdiction of                    (I.R.S. Employer Identification No.)
 incorporation or organization)
</TABLE>

                                 Trust Division
                         U.S. Bank National Association
                               1700 Farnam Street
                              Omaha, Nebraska 68102
                        --------------------------------
                    (Address of Principal Executive Offices)

                                 (402) 348-6000
                       -----------------------------------
                (Registrant's telephone no. including area code)


          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
                                              -----

                    APPLICABLE ONLY TO CORPORATE REGISTRANTS

          Indicate the number of shares outstanding of each of the registrant's
classes of common stock, as of the latest practicable date.

          As of March 31, 2000, there were 12,633,432 Units of Beneficial
Interest of the registrant outstanding.



<PAGE>   2




                         PART I - FINANCIAL INFORMATION

ITEM 1.  FINANCIAL STATEMENTS.

                              KIEWIT ROYALTY TRUST
                STATEMENT OF ASSETS, LIABILITIES AND TRUST CORPUS
                   as of March 31, 2000 and December 31, 1999

<TABLE>
<CAPTION>
ASSETS                                                                2000                  1999
------                                                           -------------         -----------
<S>                                                             <C>                     <C>
Cash equivalents                                                    $2,157,528            $253,524

Royalty and overriding
royalty interests in coal
leases                                                                 167,817             167,817

Less accumulated amortization                                         (113,010)           (111,175)
                                                                    ----------            ---------

Net royalty and overriding
royalty interests in coal leases                                        54,807              56,642
                                                                    ----------            ---------

Total Assets                                                        $2,212,335            $310,166
                                                                    ==========            ========



LIABILITIES AND TRUST CORPUS
----------------------------

Distributions payable to Unit Holders                               $2,157,528            $253,524

Trust corpus: 12,633,432 units of beneficial interest
authorized and outstanding                                              54,807              56,642
                                                                    ----------            ---------

Total Liabilities and Trust Corpus                                  $2,212,335            $310,166
                                                                    ==========            ========
</TABLE>


                   The accompanying notes are an integral part
                           of the financial statements

                                      -2-
<PAGE>   3


                              KIEWIT ROYALTY TRUST
                        STATEMENT OF DISTRIBUTABLE INCOME
               for the three months ended March 31, 2000 and 1999


<TABLE>
<CAPTION>
                                              Three Months Ended March 31
                                              ---------------------------

                                             2000                  1999
                                             ----                  ----

<S>                                      <C>                   <C>
Royalty income                            $2,158,466            $1,774,480

Interest income                               18,255                12,637

Trust expenses                               (19,193)              (18,461)
                                          ----------            ----------
Distributable income                      $2,157,528            $1,768,656


Distributable income per unit
(12,633,432 Units
Outstanding)                               $.1707792              $.139998
</TABLE>



                      STATEMENT OF CHANGES IN TRUST CORPUS
               for the three months ended March 31, 2000 and 1999


<TABLE>
<CAPTION>

                                               Three Months Ended March 31
                                               ---------------------------

                                                2000                  1999
                                                ----                  ----
<S>                                     <C>                   <C>
Trust corpus as of January 1             $      56,642         $      69,115

Amortization of royalty interests               (1,835)               (1,768)

Distributable income                         2,157,528             1,768,656

Distributions to Unit Holders               (2,157,528)           (1,768,656)
                                           -----------           -----------

Trust corpus as of March 31              $      54,807         $      67,347
                                          ============          ============
</TABLE>



                   The accompanying notes are an integral part
                           of the financial statements

                                      -3-
<PAGE>   4



                              KIEWIT ROYALTY TRUST
                          NOTES TO FINANCIAL STATEMENTS
                   as of March 31, 2000 and December 31, 1999

BASIS OF PRESENTATION

          The accompanying unaudited financial statements have been prepared in
accordance with the instructions for Form 10-Q and do not necessarily include
all of the information and footnotes required by generally accepted accounting
principles for complete financial statements. In the Trustee's opinion, all
adjustments necessary for a fair presentation have been included. For further
information, refer to the financial statements and footnotes included in the
Trust's annual report on Form 10-K for the year ended December 31, 1999.

SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

          The accompanying unaudited financial statements have been prepared on
the following basis:

      (a)      The royalty income recorded for a month is the amount received
               from the lease holder to the Trustee for such month.

      (b)      Trust administration expenses are recorded in the month they
               accrue.


This basis for reporting royalty income is thought to be the most meaningful
because distributions to unit holders for a month are based on net cash receipts
for such month. However, these statements differ from financial statements
prepared in accordance with accounting principles generally accepted in the
United States because under such principles royalty income for a month would be
based on production for such month without regard to when royalty payments are
received. In addition, amortization of the net royalty and overriding royalty
interests, which is calculated on a units-of-production basis by lease, is
charged directly to trust corpus, since such amount does not affect
distributable income.


                                       4
<PAGE>   5


ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND
RESULTS OF OPERATIONS.


            a.   MATERIAL CHANGES IN FINANCIAL CONDITION.

                 Kiewit Royalty Trust is a royalty trust with royalty and
overriding royalty interests in certain coal leases. The Trust was formed for
the purposes of (1) administering the income received from such coal leases and
(2) distributing such income (together with interest earned thereon less payment
of or provision for obligations) to the holders of the Units of Beneficial
Interest.


            b.   MATERIAL CHANGES IN RESULTS OF OPERATIONS.

                 During the first quarter of 2000, the Trust received a total of
$2,158,466 of royalty and overriding royalty payments. The following schedule
reflects the royalty and overriding royalty payments received by the Trust in
respect of leases at the following mines:

<TABLE>
<CAPTION>
Mine                                                   First Quarter
----                                       ------------------------------------
                                                 2000                 1999
                                                 ----                 ----
<S>                                           <C>                  <C>
Decker                                        $2,099,374           $1,712,181

Big Horn                                      $   59,092           $   62,299

Spring Creek                                     $   ---              $   ---
                                                 -------              -------

                                              $2,158,466           $1,774,480
                                              ==========           ==========
</TABLE>


               i.   DECKER MINE.

                    The amount of royalties and overriding royalties received by
the Trust with respect to the Decker Mine increased to $2,099,374 in the first
quarter of 2000 compared to $1,712,181 during the same period in 1999. These
changes in royalty and overriding royalty amounts received were due to changes
in the relative amounts of coal mined under leases bearing high and low
overriding royalty rates per ton, which are a normal result of the execution of
a mining plan encompassing several coal leases bearing different royalty rates.


                                       5
<PAGE>   6


               ii.  BIG HORN MINE.

                    Overall royalties received from the Big Horn Mine decreased
to $59,092 during the first quarter of 2000 from $62,299 for the same period in
1999. The decrease for 2000 reflects decreased production in the relative
amounts of coal mined under leases bearing high and low overriding rates per
ton.

              iii.  SPRING CREEK MINE.

                    No royalties were received from the Spring Creek Mine during
the first quarters of 2000 and 1999 because royalties are typically paid by the
mine operators on an annual basis during the second half of a calendar year.

                                      -6-
<PAGE>   7


                          PART II - OTHER INFORMATION.

ITEM 1.     LEGAL PROCEEDINGS.
            There are no material pending legal proceedings to which the Trust
is a party or which any of its property is the subject.

ITEM 6. EXHIBITS AND REPORTS ON FORM 8-K.

            (a)         Exhibits

                        4.1            Kiewit Royalty Trust Indenture dated May
                                       17, 1982, as amended June 9, 1982 and
                                       June 23, 1982 (filed as Exhibit 1 to the
                                       Trust's Form 10 filed with the Securities
                                       and Exchange Commission on December 23,
                                       1982, and incorporated herein by
                                       reference).

                        4.2            Order dated September 23, 1994, of the
                                       County Court of Douglas County, Nebraska
                                       (filed as Exhibit 2 to the Trust's Form
                                       10-Q filed with the Securities and
                                       Exchange Commission on November 14, 1994,
                                       and incorporated herein by reference).

                        27.1           Financial Data Schedule.

            (b)         No reports on Form 8-K were filed during the quarter for
which this report is filed.

                                      -7-
<PAGE>   8


                                    SIGNATURE
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.
                        KIEWIT ROYALTY TRUST
                        (Registrant)

                        By:  U. S. Bank National Association
                        in its capacity as
                        Trustee and not in its individual capacity or otherwise



                        By:     /S/ Susan K. Rosburg
                                ------------------------
                                Susan K. Rosburg
                                Trust Officer


Dated: May 11, 2000

                                      -8-