<PAGE>   1
                                   FORM 10-Q

                       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 September 30, 1995

                          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>


                          FirsTier Bank N.A. Omaha
                            17th & Farnam Streets
                           Omaha, Nebraska  68102
                   ---------------------------------------
                  (Address of Principal Executive Offices)

                               (402) 348-6275
           ------------------------------------------------------
              (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 September 30, 1995, 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, LIABILITY AND TRUST CORPUS

                 as of September 30, 1995 and December 31, 1994

<TABLE>
<CAPTION>
                                                 SEPTEMBER 30,               DECEMBER 31,
ASSETS                                              1995                         1994       
------                                         -----------------           ---------------
<S>                                          <C>                         <C>
Cash and short-term investments              $  3,426,087                $    398,618

Net royalty and overriding
royalty interests in coal
leases:

Estimated fair market value
at date of transfer to Trust                        $ 73,878,000                $ 73,878,000

Allowance to reduce carrying
value to Peter Kiewit Sons'
Inc.'s historical book value                       ( 73,710,183)                (73,710,183)
                                                   -------------               -------------

                                                   $    167,817                $    167,817

Less accumulated amortization                           (68,995)                    (58,995)


Net royalty and overriding
royalty interests in coal
leases                                             $     98,822                $    108,822
                                                   ------------                ------------

Total Assets                                       $  3,524,909                $    507,440
                                                   ============                ============

LIABILITY AND TRUST CORPUS
--------------------------

Distributions payable to
Unit Holders                                       $  3,426,087                $    398,618

Trust corpus: 12,633,432
units of beneficial interest
authorized and outstanding                         $     98,822                $    108,822
                                                    -----------                 -----------

Total Liability and Trust Corpus             $  3,524,909                $    507,440
                                             ============                ============
</TABLE>


                  The accompanying notes are an integral part
                          of the financial statements
<PAGE>   3
                              KIEWIT ROYALTY TRUST


                       STATEMENT OF DISTRIBUTABLE INCOME

     For the Three Months and Nine Months Ended September 30, 1995 and 1994

<TABLE>
<CAPTION>
                                 Three Months Ended                    Nine Months Ended
                                    September 30                          September 30      
                              ------------------------             ---------------------------

                               1995            1994                  1995            1994     
                            ------------   ------------           -------------   ------------
<S>                     <C>                   <C>                 <C>            <C>
Royalty Income                 $ 3,405,049    $ 3,044,840          $ 7,313,800   $ 7,266,502

Net received
escrow funds 1/                   --              537,454             --             174,218

Interest income                     32,990         67,788               87,629        93,675

Trust expenses                    (11,952)       (16,166)             (29,339)      (42,202)
                             -------------   ------------         ------------  ------------

Distributable
Income                        $  3,426,087   $  3,633,916         $  7,372,090  $  7,492,193
                              ============   ============         ============  ============

Distributable Income
per Unit (12,633,432
Units)                        $    .271192   $    .287643         $    .583538  $    .593045
</TABLE>

                 See Accompanying Notes to Financial Statements





------------------------

1/  All amounts received from escrow were received during the third quarter. 
The amount of "Net Received Escrowed Funds" shown for each period includes funds
received from escrow during the relevant period that were not attributable to
royalties received during that period.  The amount shown as received during the
first nine months of 1994 is smaller than the amount shown as received during
the third quarter of 1994 because escrowed funds in the amount of $363,236 are
attributable to royalty income for the first six months of 1994 and thus
included in "Royalty Income" for the first nine months of 1994.

                                     - 2 -
<PAGE>   4
                              KIEWIT ROYALTY TRUST

                      STATEMENT OF CHANGES IN TRUST CORPUS

             For the Nine Months Ended September 30, 1995 and 1994

<TABLE>
<CAPTION>
                                            1995                1994    
                                        -----------         ------------
<S>                                    <C>                  <C>
Trust Corpus as of
   January 1                           $   108,822          $   129,396

Amortization of
   royalty interest                       (10,000)             (12,235)

Distributable Income                     7,372,090            7,492,193

Distribution to Unit
   Holders                             (7,372,090)          (7,492,193)
                                      ------------         ------------

Trust Corpus as of
   September 30                        $    98,822          $   117,161
                                       ===========          ===========
</TABLE>

                 See Accompanying Notes to Financial Statements





                                     - 3 -
<PAGE>   5
                              KIEWIT ROYALTY TRUST

                         Notes to Financial Statements
                 as of September 30, 1995 and December 31, 1994

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, 1994.

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
                      computed and paid by 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 the 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 generally accepted accounting principles
because, under such principles, royalty income for a month would be based on
production for such month without regard to when calculated or 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>   6
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 nine months ended September 30, 1995, the Trust
received a total of $7,313,800 of royalty and overriding royalty payments;
during the three months ended September 30, it received a total of $3,405,049
of such payments.  The following schedule reflects the royalty and overriding
royalty amounts received by the Trust from each mine.

<TABLE>
<CAPTION>
 Mine                              Three Months Ended                Nine Months Ended
 ----                                 September 30                     September 30                                                
                                   -------------------              --------------------
                                   1995          1994               1995          1994
                                   ----          ----               ----          ----
 <S>                             <C>          <C>                 <C>           <C>
 Decker                          $2,338,528   $2,160,590          $5,644,098    $5,897,293
 Spring Creek                       913,096      793,375             913,096       793,375
 Black Butte                        144,277       82,459             638,937       445,695
 Big Horn                             9,148        8,416             117,669       130,139
                                 ----------   ----------          ----------    ----------

                                 $3,405,049   $3,044,840          $7,313,800    $7,266,502
                                 ==========   ==========          ==========    ==========
</TABLE>


                 i.       DECKER MINE

                 The amount of royalties and overriding royalties received by
the Trust with respect to the Decker Mine decreased to $5,644,098 in the nine
months ended September 30, 1995 compared to $5,897,293 during the same period
in 1994.  For the third quarter of 1995, the amounts received increased to
$2,338,528 compared to $2,160,590 during the third quarter of 1994.  These
variations in receipts during the nine months and three months ended September
30, 1995 were due to changes in the relative amounts of coal mined under





                                     - 5 -
<PAGE>   7
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.

                 ii.      SPRING CREEK MINE

                 Royalties received from the Spring Creek Mine increased from
$793,375 during the nine months ended September 30, 1994 to $913,096 during the
corresponding period in 1995.  The Trust received $913,096 in the third quarter
of 1995, compared to $793,375 during the third quarter of 1994.  This increase
reflects increased production from the applicable lease.  Royalties from the
Spring Creek Mine are typically paid by the mine operators on an annual basis
during the second half of the calendar year.

                 iii.     BLACK BUTTE MINE

                 The Trust received $638,937 in royalty and overriding royalty
amounts from the Black Butte Mine during the nine months ended September 30,
1995, an increase from the $445,695 received during the nine months ended
September 30, 1994.  Of the $445,695 in royalties received during the first
nine months of 1994, $404,475 was originally paid into escrow, then released to
the Trust during the third quarter of 1994.  The Trust received $144,277 during
the third quarter of 1995, as compared to receipts of $82,459 during the third
quarter of 1994.  Of the $82,459 in royalties received during the third quarter
of 1994, $41,239 was originally paid into escrow, then released to the Trust
during the third quarter of 1994.  The increase in receipts during the third
quarter of 1995 was 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.

                 Lease number W-6266 provides that the terms and conditions of
the lease are subject to "reasonable readjustment" effective on April 1, 1996.
At that time, the royalty rate payable to the United States will be increased
to 12- 1/2%, which is the currently prevailing federal royalty rate.  Because
of the cap on the amount of the overriding royalty payable to the Trust with
respect to this lease, the increased royalty rate will effectively eliminate
further payments to the Trust with respect to that lease.





                                     - 6 -
<PAGE>   8
                 vi.      BIG HORN MINE

                 Overall royalties received from the Big Horn Mine decreased to
$117,669 during the nine months ended September 30, 1995 from $130,139 in 1994,
and increased to $9,148 in the third quarter of 1995 from $8,416 in the third
quarter of 1994.  The decrease in the first nine months of 1995 reflects
decreased production from the applicable leases.  The Trustee anticipates that
there will be minimal production at the Big Horn Mine in the future.

                          PART II - OTHER INFORMATION.

ITEM 1.  LEGAL PROCEEDINGS.

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

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

         (a)     Exhibits.

                 27     Financial Data Schedule.

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





                                     - 7 -
<PAGE>   9
                                   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:     FirsTier Bank N.A. Omaha in
                                        its capacity as Trustee and not
                                        in its individual capacity or
                                        otherwise
                                
                                
                                
                                        By:  /s/   Susan K. Rosburg 
                                            ------------------------
                                            Susan K. Rosburg
                                            Trust Officer



Dated:  November 14, 1995