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

                                       2
<PAGE>

                      TEXLAND DRILLING PROGRAM - 1981, LTD.
                             (A LIMITED PARTNERSHIP)

                                 BALANCE SHEETS
                       June 30, 1998 and December 31, 1997
                                   (Unaudited)

<TABLE>
<CAPTION>


ASSETS

                                                                   6/30/98      12/31/97
                                                               -----------   -----------
<S>                                                            <C>           <C>    
CURRENT ASSETS
    Cash                                                       $    15,524   $    63,132
    Accounts Receivable
       Trade                                                        71,143       117,054
       General Partner                                                   -             -
                                                               -----------   -----------
       Total Current Assets                                         86,667       180,186

PROPERTY AND EQUIPMENT, AT COST
    (SUCCESSFUL EFFORTS METHOD)
    Intangible Development Costs                                 7,857,131     7,856,354
    Lease and Well Equipment                                     4,574,350     4,562,176
    Producing Leaseholds                                           373,226       373,188
                                                               -----------   -----------
                                                                12,804,707    12,791,718
    Less: Accumulated Depreciation, Depletion & Amortization    10,002,865     9,845,056
                                                               -----------   -----------
 
                                                                 2,801,842     2,946,662
    Wells-in-Progress
    Nonproducing Leaseholds                                              -             -
                                                               -----------   -----------
       Net Property, Plant and Equipment                         2,801,842     2,946,662

Organizational Costs (net of $1,141,028 amortization in 1991
    and $1,069,798 in 1990)                                              -             -
                                                               -----------   -----------
    Total Assets                                               $ 2,888,509   $ 3,126,848
                                                               ===========   ===========
 

LIABILITIES AND PARTNERS' EQUITY

CURRENT LIABILITIES
    Accounts Payable - Trade                                        49,736        49,218
                                                               -----------   -----------
    Total Current Liabilities                                       49,736        49,218

PARTNERS' EQUITY
    Limited Partners - 2,425 Units Outstanding                   2,059,557     2,232,831
    General Partner                                                779,216       844,799
                                                               -----------   -----------
    Total Partners' Equity                                       2,838,773     3,077,630
                                                               -----------   -----------
    Total Liabilities and Partners' Equity                       2,888,509     3,126,848
                                                               ===========   ===========
</TABLE>

                            See Accompanying Notes

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

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

<TABLE>
<CAPTION>


                                                                             Three Months Ended                 Six Months Ended
                                                                                  June 30,                           June 30,
                                                                            1998             1997             1998            1997
                                                                       ---------        ---------        ---------       ---------
<S>                                                                    <C>              <C>              <C>             <C>    
REVENUES
    Oil and Gas Sales                                                  $ 229,005        $ 331,620        $ 494,751       $ 736,240
    Interest Income                                                          306              379              745           1,002
    Gain on Sale                                                               -                -                -               -
                                                                       ---------        ---------        ---------       ---------
                                                                         229,310          331,999          495,495         737,242

EXPENSES
    Fees to Managing General Partner                                      19,730           26,700           43,990          46,300
    Production Expenses                                                  149,868          134,999          273,194         270,450
    Severance Tax Withholding                                             10,534           15,255           22,759          33,867
    Depreciation, Depletion & Amortization Expenses                       78,905           75,581          157,809         151,162
    Other Expenses                                                        11,996            9,965           13,687           9,965
                                                                       ---------        ---------        ---------       ---------
                                                                         271,033          262,500          511,439         511,744
                                                                       ---------        ---------        ---------       ---------
NET INCOME (LOSS)                                                      $ (41,723)       $  69,499        $ (15,944)      $ 225,497
                                                                       ---------        ---------        ---------       ---------

NET INCOME (LOSS) ALLOCATION
    Limited Partners                                                     (33,335)          18,290          (27,699)         86,871
    General Partner                                                       (8,388)          48,804           11,755         134,990
                                                                       ---------        ---------        ---------       ---------
                                                                       $ (41,723)       $  67,095        $ (15,944)      $ 221,861
                                                                       ---------        ---------        ---------       ---------
NET INCOME (LOSS) PER $5,000 LIMITED PARTNER UNIT
    (2,425 Units Outstanding)                                          $     (14)       $       8        $     (11)      $      36
                                                                       ---------        ---------        ---------       ---------
</TABLE>

                             See Accompanying Notes

                                       4
<PAGE>

                      TEXLAND DRILLING PROGRAM - 1981, Ltd.
                             (A LIMITED PARTNERSHIP)

                          STATEMENT OF PARTNERS' EQUITY
                         Six Months Ended June 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                               12,212                                     12,212

Partners' Distributions                             (235,125)            (138,225)              (96,900)

Net Income (Loss)                                    (15,944)             (27,699)               11,755
                                                 -----------          -----------             ---------        
BALANCE JUNE 30, 1998                            $ 2,838,773          $ 2,059,557             $ 779,216
                                                 ===========          ===========             =========  
</TABLE>      

                             See Accompanying Notes

                                       5

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

                             STATEMENTS OF CASH FLOW
                     Six Months Ended June 30, 1998 and 1997
                                   (Unaudited)
<TABLE>
<CAPTION>

                                                                                               1998                 1997
                                                                                          ---------            ---------
<S>                                                                                       <C>                  <C>    
                        
CASH FLOWS FROM OPERATING ACTIVITIES
   Net Income (Loss)                                                                      $ (15,944)           $ 221,861
   Adjustments to Reconcile Net Income to Net Cash Provided by
       Operating Activities:
       Depreciation, Depletion and Amortization Expenses                                    157,809              151,162
       Abandoned Leaseholds
       Loss on Sale of Assets
       Change in Accounts Receivable                                                         45,911               73,963
       Change in Accounts Payable                                                               518               26,492
                                                                                          ---------            ---------
       Total Adjustments                                                                    204,238              251,617
                                                                                          ---------            ---------
       Net Cash Provided by Operating Activities                                            188,294              473,479

CASH FLOWS FROM INVESTING ACTIVITIES
   Acquisition of Property and Equipment                                                    (12,989)            (177,811)
   Proceeds from Sale of Property and Equipment                                                   -                    -
                                                                                          ---------            ---------
       Net Cash Used by Investing Activities                                                (12,989)            (177,811)

CASH FLOWS FROM FINANCING ACTIVITIES
   Partners' Contributions                                                                   12,212               74,353
   Partners' Distributions                                                                 (235,125)            (437,400)
                                                                                          ---------            ---------
       Net Cash Used by Financing Activities                                               (222,913)            (363,047)

NET INCREASE IN CASH                                                                        (47,608)             (67,380)
Cash at Beginning of Year                                                                    63,132               92,858
                                                                                          ---------            ---------
CASH AT END OF QUARTER                                                                    $  15,524            $  25,478
                                                                                          =========            =========
</TABLE>

                             See Accompanying Notes

                                       6
<PAGE>
 
                      TEXLAND DRILLING PROGRAM-1981, LTD.
                            (A LIMITED PARTNERSHIP)
                             
                                        
                         NOTES TO FINANCIAL STATEMENTS
                                 June 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
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
                                 June 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 six months ended June 30, 1998  and June 30, 1997, the Partnership was
charged $46,298 and $36,812 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 
                     CONDITIONS AND RESULTS OF OPERATIONS

                                 June 30, 1998


The Partnership's average price per barrel of oil for the second quarter of 1998
was $9.09 as compared to $15.19 for the second quarter of 1997. The decreased
revenue results primarily from the decrease in average oil prices.

Production expenses for 1998 increased from the comparable period in 1997, due
to an increase in the costs of oil field services.

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: August 7, 1998

                                       10