<PAGE>
 
                      SECURITIES AND EXCHANGE COMMISSION

                            Washington, D. C. 20549

                                   Form 10-Q

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


For the Quarter ended
 September 30, 1998                               Commission File Number 2-71865
---------------------                             ------------------------------

                      TEXLAND DRILLING PROGRAM-1981, LTD.
                      -----------------------------------
                             (Name of Registrant)


         TEXAS                                            75-1791491
-----------------------                     ------------------------------------
(State of Organization)                     (I.R.S. Employer Identification No.)

500 Throckmorton Street, Suite 3100
        Fort Worth, Texas                                                76102
-----------------------------------                                     --------
  (Address of Executive Offices)                                        Zip Code

                 Registrant's Telephone Number   (817) 336-2751
                                                 --------------

          Securities registered pursuant to Section 12(b) of the Act:

Units of Limited Partnership Interest                                  None
-------------------------------------                             --------------
         (Title of Class)                                         (Voting Units)


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
        -----   -----

                   This report contains a total of 10 pages.

                                       1
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                                        
                         INDEX TO FINANCIAL STATEMENTS
                                        

                                Reference Page
                                --------------

Balance Sheets at September 30, 1998 and                                       3
    December 31, 1997.
 
Statements of Operations for the Nine Months                                   4
    Ended September 30, 1998 and 1997.
 
Statement of Partners' Equity at September 30, 1998.                           5
 
Statements of Cash Flows for Nine Months Ended                                 6
    September 30, 1998 and 1997.
 
Notes to Financial Statements.                                               7-8

                                       2
<PAGE>
                     TEXLAND DRILLING PROGRAM - 1981, LTD.
                            (A LIMITED PARTNERSHIP)

                                BALANCE SHEETS
                   September 30, 1998 and December 31, 1997
                                  (Unaudited)
<TABLE>
<CAPTION>
ASSETS
                                                                               9/30/98            12/31/97
                                                                             -----------         -----------
<S>                                                                          <C>                 <C>
CURRENT ASSETS
    Cash                                                                     $    48,229         $    63,132
    Accounts Receivable
       Trade                                                                      67,747             117,054
       General Partner                                                                 -                   -
                                                                             -----------         -----------
       Total Current Assets                                                      115,976             180,186

PROPERTY AND EQUIPMENT, AT COST
    (SUCCESSFUL EFFORTS METHOD)
    Intangible Development Costs                                               7,857,131           7,856,354
    Lease and Well Equipment                                                   4,582,228           4,562,176
    Producing Leaseholds                                                         373,226             373,188
                                                                             -----------         -----------
                                                                              12,812,585          12,791,718
    Less: Accumulated Depreciation, Depletion & Amortization                  10,081,769           9,845,056
                                                                             -----------         -----------
                                                                               2,730,816           2,946,662
    Wells-in-Progress
    Nonproducing Leaseholds                                                            -                   -
                                                                             -----------         -----------
       Net Property, Plant and Equipment                                       2,730,816           2,946,662

Organizational Costs (net of $1,141,028 amortization in 1991
    and $1,069,798 in 1990)                                                            -                   -
                                                                             -----------         -----------
    Total Assets                                                             $ 2,846,792         $ 3,126,848
                                                                             ===========         ===========

LIABILITIES AND PARTNERS' EQUITY

CURRENT LIABILITIES
    Accounts Payable - Trade                                                      76,060              49,218
                                                                             -----------         -----------
    Total Current Liabilities                                                     76,060              49,218

PARTNERS' EQUITY
    Limited Partners - 2,425 Units Outstanding                                 2,013,438           2,232,831
    General Partner                                                              757,293             844,799
                                                                             -----------         -----------
    Total Partners' Equity                                                     2,770,732           3,077,630
                                                                             -----------         -----------
    Total Liabilities and Partners' Equity                                     2,846,792           3,126,848
                                                                             ===========         ===========
</TABLE> 

                            See Accompanying Notes

                                       3
<PAGE>
 
                     TEXLAND DRILLING PROGRAM - 1981, LTD.
                            (A LIMITED PARTNERSHIP)

                            STATEMENT OF OPERATIONS
                          September 30, 1998 and 1997
                                  (Unaudited)

<TABLE>
<CAPTION>
                                                                 Three Months Ended         Nine Months Ended
                                                                    September 30,             September 30,
                                                                 1998          1997         1998          1997
                                                               --------      --------     --------     ----------
<S>                                                            <C>           <C>          <C>          <C> 
REVENUES
   Oil and Gas Sales                                           $205,288      $441,758     $700,038     $1,168,840
   Interest Income                                                  212           893          957          2,210
   Gain on Sale                                                  26,368             -       26,368              -
                                                               --------      --------     --------     ----------
                                                                231,867       442,651      727,363      1,171,050
                                                               --------      --------     --------     ----------

EXPENSES                                                                                               
   Fees to Managing General Partner                              28,020        16,050       72,010         48,150
   Production Expenses                                          129,946       112,264      403,140        330,680
   Severance Tax Withholding                                      9,443        21,859       32,202         55,305
   Depreciation, Depletion & Amortization Expenses               78,905        89,066      236,714        267,199
   Other Expenses                                                 2,061        (6,947)      15,748         14,378
                                                               --------      --------     --------     ----------
                                                                248,374       232,292      759,814        715,712
                                                               --------      --------     --------     ----------
 NET INCOME (LOSS)                                             $(16,507)     $210,359     $(32,451)    $  455,338
                                                               --------      --------     --------     ----------

NET INCOME (LOSS) ALLOCATION                                                                           
   Limited Partners                                             (15,806)      105,336      (43,505)       208,892
   General Partner                                                 (701)      105,024       11,054        246,445
                                                               --------      --------     --------     ----------
                                                               $(16,507)     $210,360     $(32,451)    $  455,337
                                                               --------      --------     --------     ----------
NET INCOME (LOSS) PER $5,000 LIMITED PARTNER UNIT                                                      
   (2,425 UNITS OUTSTANDING)                                   $     (7)     $     43     $    (18)    $       86
                                                               --------      --------     --------     ----------
</TABLE>

                            See Accompanying Notes

                                       4
<PAGE>
 
                    TEXLAND DRILLING PROGRAM  - 1981, LTD.
                            (A LIMITED PARTNERSHIP)
 
                         STATEMENT OF PARTNERS' EQUITY
                     Nine Months Ended September 30, 1998
                                  (Unaudited)
<TABLE> 
<CAPTION> 
                                                    Limited          General
                                    Total           Partner          Partner
                                  ----------       ----------       --------- 
<S>                               <C>              <C>              <C> 
BALANCE DECEMBER 31, 1997         $3,077,630       $2,225,481       $ 852,149
                                                                    
Partners' Contributions               20,090                           20,090
                                                                    
Partners' Distributions             (294,538)        (168,538)       (126,000)
                                                                    
Net Income (Loss)                    (32,451)         (43,505)         11,054
                                  ----------       ----------       --------- 
BALANCE SEPTEMBER 30, 1998        $2,770,732       $2,013,438       $ 757,293
                                  ==========       ==========       ========= 
</TABLE>

                            See Accompanying Notes

                                       5
<PAGE>
                     TEXLAND DRILLING PROGRAM - 1981, LTD.
                            (A LIMITED PARTNERSHIP)

                            STATEMENTS OF CASH FLOW
                 Nine Months Ended September 30, 1998 and 1997
                                  (Unaudited)
<TABLE>
<CAPTION>
                                                                                            1998                 1997
                                                                                          ---------            ---------
<S>                                                                                            <C>                  <C> 
CASH FLOWS FROM OPERATING ACTIVITIES
   Net Income (Loss)                                                                      $ (32,451)           $ 321,909
   Adjustments to Reconcile Net Income to Net Cash Provided by
       Operating Activities:
       Depreciation, Depletion and Amortization Expenses                                    236,714              226,743
       Abandoned Leaseholds
       Loss on Sale of Assets
       Change in Accounts Receivable                                                         49,307               69,571
       Change in Accounts Payable                                                            26,842               35,709
                                                                                          ---------            ---------
       Total Adjustments                                                                    312,863              332,023
                                                                                          ---------            ---------
       Net Cash Provided by Operating Activities                                            280,412              653,932

CASH FLOWS FROM INVESTING ACTIVITIES
   Acquisition of Property and Equipment                                                    (20,867)            (230,993)
   Proceeds from Sale of Property and Equipment                                                   -                    -
                                                                                          ---------            ---------
       Net Cash Used by Investing Activities                                                (20,867)            (230,993)

CASH FLOWS FROM FINANCING ACTIVITIES
   Partners' Contributions                                                                   20,090               93,953
   Partners' Distributions                                                                 (294,538)            (555,650)
                                                                                          ---------            ---------
       Net Cash Used by Financing Activities                                               (274,447)            (461,697)

NET INCREASE IN CASH                                                                        (14,903)             (38,758)
Cash at Beginning of Year                                                                    63,132               92,858
                                                                                          ---------            ---------
CASH AT END OF QUARTER                                                                    $  48,229            $  54,100
                                                                                          =========            =========
</TABLE>

                            See Accompanying Notes

                                       6
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A LIMITED PARTNERSHIP)
                                        
                         NOTES TO FINANCIAL STATEMENTS
                              September 30, 1998
                                  (Unaudited)



1.  SUMMARY OF SIGNIFICANT ACCOUNTING POLICIES

The Partnership was organized as a limited partnership on June 20, 1981 for the
purpose of engaging in oil and gas exploration and production.  Texland
Properties-1981, a general partnership, and Texland Petroleum, Inc. are the
General Partners.  The Managing General Partner is Texland Petroleum, Inc.  The
Partnership's accounting policies are summarized below:

BASIS OF ACCOUNTING
The Partnership follows generally accepted accounting principles applicable to
established enterprises in the extractive industries under a method which is
generally known as the successful method of accounting.

PROPERTY AND EQUIPMENT
Costs incurred for the acquisition of producing and nonproducing leaseholds are
capitalized.  Costs of intangible development and lease and well equipment
incurred to drill and equip successful exploratory and development wells are
capitalized.  Costs to drill and equip unsuccessful exploratory wells are
charged to operations while costs of unsuccessful development wells remain
capitalized.  Costs associated with uncompleted wells are capitalized as wells-
in-progress.

ABANDONED LEASEHOLDS
Costs of nonproducing properties are charged to expense at such time as they are
deemed to be impaired, based upon periodic assessments of such costs.

DEPLETION
Leasehold costs of producing properties are amortized on the unit of production
method based on proved oil and gas reserves.  Intangible development costs of
producing properties are amortized on the unit of production method based on
estimated proved developed oil and gas reserves.

DEPRECIATION
Depreciation of equipment is provided by using the unit of production method
based on estimated proved developed oil and gas reserves.

ORGANIZATION COSTS
These costs are amortized by the straight-line method over ten years, the life
of the Partnership.

FEDERAL INCOME TAX
The Partnership files its federal income tax return on the accrual basis.

                                       7
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A LIMITED PARTNERSHIP)
                                        
                   NOTES TO FINANCIAL STATEMENTS (CONTINUED)
                              September 30, 1998
                                  (Unaudited)



2.  CONTRIBUTIONS BY GENERAL PARTNER (TEXLAND PROPERTIES-1981)

Under terms of the Partnership Agreement, the General Partner is charged for
certain costs related to drilling and production operations which are required
to be capitalized for federal income tax purposes.  These costs are treated as
capital contributions by the General Partner.  In addition, Texland Properties-
1981 and Texland Petroleum, Inc. have invested in limited partnership units in
the amount of $95,000 and $30,000 respectively.

3.  FEES TO MANAGING GENERAL PARTNER (TEXLAND PETROLEUM, INC.)

In consideration of its management services rendered, the Managing General
Partner is entitled to charge management fees to the Partnership.  In addition,
for the nine months ended September 30, 1998  and September 30, 1997, the
Partnership was charged $69,447 and $110,436 respectively for technical
services, accounting services, and supervisory services performed by the
employees of the Managing General Partner and such charges are included in
intangible development costs, production expenses and fees to Managing General
Partner.  These charges are allocated between the General and Limited Partners
based upon applicable revenue and expense sharing rates.

                                       8
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A LIMITED PARTNERSHIP)
                                        
               MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL
                      CONDITION AND RESULTS OF OPERATIONS

                              September 30, 1998



The Partnership's average price per barrel of oil for the third quarter of 1998
was $8.44 as compared to $14.74 for the third quarter of 1997. The decreased
revenue and related severance tax expense result primarily from the decrease in
average oil prices.

Production expenses for 1998 increased from the comparable period in 1997, due
to increased remedial workover activity and, in particular, a significant
workover expenditure on a deep South Texas gas well in which the Partnership has
a substantial interest.

The Partnership was formed with cash contributions from the Limited and General
Partners.  Management does not intend to incur any substantial indebtedness and
any developmental drilling which is necessary will be processed by farmout to
other parties or by reinvestment of internally generated funds.  Management,
therefore, anticipates no liquidity problems during the life of the Partnership.

                                       9
<PAGE>
 
PART II


Items 1 through 6
-----------------

Omitted - Not applicable to Registrant.


                                   SIGNATURE
                                   ---------
                                        

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


                                        Texland Drilling Program-1981, Ltd.



                                        By /s/ M. E. Chapman
                                          --------------------------------------
                                          M. E. Chapman, Vice President
                                          of Texland Petroleum, Inc.,
                                          General Partner - Texland
                                          Properties-1981


Date: November 13, 1998

                                       10