<PAGE>   1
                       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 Period Ended March 31, 1998               Commission File Number 0-18927


                         TANDY BRANDS ACCESSORIES, INC.
             (Exact name of registrant as specified in its charter)

         Delaware                                                 75-2349915
(State or other jurisdiction of                               (I.R.S. Employer
incorporation or organization)                               Identification No.)


690 East Lamar Boulevard, Suite 200, Arlington, TX                  76011
   (Address of principal executive offices)                       (Zip Code)


        Registrant's telephone number, including area code (817)-548-0090


             Former name, former address and former fiscal year, if
                           changed since last report:

                                 Not Applicable

         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

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


         Class                   Number of shares outstanding at March 31, 1998
Common stock, $1 par value                         5,576,017


<PAGE>   2


                 TANDY BRANDS ACCESSORIES, INC. AND SUBSIDIARIES

                                    Form 10-Q

                          Quarter Ended March 31, 1998


                                TABLE OF CONTENTS

PART I -- FINANCIAL INFORMATION

<TABLE>
<CAPTION>
Item                                                                       Page No.
                                                                           --------
<S>                                                                         <C>
1.       Financial Statements                                               3 - 7

2.       Management's Discussion and Analysis of Financial Condition
         and Results of Operations                                          8 - 9


PART II -- OTHER INFORMATION

Item

6.       Exhibits and Reports on Form 8-K                                     10


         SIGNATURES                                                           11


         INDEX TO EXHIBITS                                                    12
</TABLE>




                                       2
<PAGE>   3
                TANDY BRANDS ACCESSORIES, INC. AND SUBSIDIARIES
                              File Number 0-18927
                                   Form 10-Q
                  Condensed Consolidated Statements of Income
                    (In thousands, except per share amounts)
                                  (Unaudited)



<TABLE>
<CAPTION>
                                                              Three Months                Nine Months
                                                                 Ended                       Ended
                                                                March 31                    March 31
                                                         -----------------------     -----------------------
                                                           1998          1997          1998          1997
                                                         ---------     ---------     ---------     ---------
<S>                                                      <C>           <C>           <C>           <C>      
 Gross sales, less discounts, returns and allowances     $  32,970     $  23,922     $ 100,658     $  77,462
 Royalty, interest and other income                             14            31           128            82
                                                         ---------     ---------     ---------     ---------
         Total revenues                                     32,984        23,953       100,786        77,544
                                                         ---------     ---------     ---------     ---------

 Costs and expenses:
     Cost of goods sold                                     20,947        14,985        63,488        48,706
     Selling, general and administrative                     8,936         6,984        25,128        20,979
     Depreciation and amortization                             463           430         1,343         1,304
     Interest expense                                          363           313           989           953
                                                         ---------     ---------     ---------     ---------
         Total costs and expenses                           30,709        22,712        90,948        71,942
                                                         ---------     ---------     ---------     ---------

 Income before provision for income taxes                    2,275         1,241         9,838         5,602
 Provision for income taxes                                    891           496         3,791         2,094
                                                         =========     =========     =========     =========
         Net income                                      $   1,384     $     745     $   6,047     $   3,508
                                                         =========     =========     =========     =========

 Earnings per common share                               $    0.25     $    0.14     $    1.09     $    0.65
                                                         =========     =========     =========     =========

 Earnings per common share - assuming dilution           $    0.24     $    0.14     $    1.07     $    0.64
                                                         =========     =========     =========     =========

 Common shares outstanding                                   5,587         5,470         5,564         5,437
                                                         =========     =========     =========     =========

 Common shares outstanding - assuming dilution               5,716         5,506         5,662         5,463
                                                         =========     =========     =========     =========


Cash dividends per common share                               None          None          None          None
</TABLE>


              The accompanying notes are an integral part of these
                        condensed financial statements.




                                       3
<PAGE>   4
                 TANDY BRANDS ACCESSORIES, INC. AND SUBSIDIARIES
                               File Number 0-18927
                                    Form 10-Q
                      Condensed Consolidated Balance Sheets
                             (Dollars in thousands)


<TABLE>
<CAPTION>
                                                                           March 31,       June 30,
                                                                             1998            1997
                                                                          ----------      ----------
 ASSETS                                                                   (Unaudited)
<S>                                                                       <C>             <C>       
 Current assets:
     Cash and cash equivalents                                            $    1,006      $      554
     Accounts receivable, net                                                 23,272          15,210
     Inventories:
         Raw materials and work in process                                     5,081           5,982
         Finished goods                                                       28,719          26,278
     Other current assets                                                      2,629           2,489
                                                                          ----------      ----------
         Total current assets                                                 60,707          50,513
                                                                          ----------      ----------

 Property and equipment, at cost                                              10,735           9,652
 Accumulated depreciation                                                     (5,523)         (4,797)
                                                                          ----------      ----------
         Net property and equipment                                            5,212           4,855
                                                                          ----------      ----------

 Other assets:
     Goodwill, less amortization                                               7,445           7,941
     Other assets, less amortization                                           2,047           2,055
                                                                          ----------      ----------
         Total other assets                                                    9,492           9,996
                                                                          ----------      ----------
 TOTAL ASSETS                                                             $   75,411      $   65,364
                                                                          ==========      ==========

 LIABILITIES AND STOCKHOLDERS' EQUITY
 Current liabilities:
     Accounts payable                                                     $    1,508      $    3,180
     Accrued expenses                                                          4,793           3,979
                                                                          ----------      ----------
         Total current liabilities                                             6,301           7,159
                                                                          ----------      ----------

 Other liabilities:
     Notes payable                                                            19,700          15,850
     Other noncurrent liabilities                                                332             226
                                                                          ----------      ----------
         Total other liabilities                                              20,032          16,076
                                                                          ----------      ----------

 Stockholders' equity:
     Preferred stock, $1 par value, 1,000,000 shares authorized,
         none issued                                                            --              --
     Common stock, $1 par value, 10,000,000 shares authorized,
         5,576,017 shares and 5,490,091 shares issued and outstanding
         as of March 31, 1998, and June 30, 1997, respectively                 5,576           5,490
     Additional paid-in capital                                               19,687          18,732
     Retained earnings                                                        23,815          17,907
                                                                          ----------      ----------
         Total stockholders' equity                                           49,078          42,129
                                                                          ----------      ----------
 TOTAL LIABILITIES AND STOCKHOLDERS' EQUITY                               $   75,411      $   65,364
                                                                          ==========      ==========
</TABLE>


              The accompanying notes are an integral part of these
                         condensed financial statements.



                                       4
<PAGE>   5
                 TANDY BRANDS ACCESSORIES, INC. AND SUBSIDIARIES
                               File Number 0-18927
                                    Form 10-Q
                 Condensed Consolidated Statements of Cash Flows
                             (Dollars in thousands)
                                  (Unaudited)



<TABLE>
<CAPTION>
                                                                                        Nine Months Ended
                                                                                            March 31,
                                                                                    --------------------------
                                                                                       1998            1997 
                                                                                    ----------      ----------
<S>                                                                                 <C>             <C>       
 Cash flows from operating activities:
     Net income                                                                     $    6,047      $    3,508
     Adjustments to reconcile net income to net cash provided by (used for)
     operating activities:
        Depreciation                                                                       828             801
        Amortization                                                                       620             640
        Other                                                                              (10)           (100)
     Change in assets and liabilities:
        Accounts receivable                                                             (8,062)         (4,192)
        Inventories                                                                     (1,540)         (7,221)
        Other assets                                                                       (86)            384
        Accounts payable                                                                (1,672)         (3,048)
        Accrued expenses                                                                   920           1,437
                                                                                    ----------      ----------
     Net cash used for operating activities                                             (2,955)         (7,791)
                                                                                    ----------      ----------

 Cash flows from investing activities:
     Purchases of property and equipment                                                (1,484)           (775)
                                                                                    ----------      ----------
     Net cash used for investing activities                                             (1,484)           (775)
                                                                                    ----------      ----------

 Cash flows from financing activities:
     Exercise of employee stock options, net of purchase of treasury stock                 222            --   
     Sale of stock to stock purchase program                                               819             611
     Proceeds from borrowings                                                           40,750          38,650
     Payments under borrowings                                                         (36,900)        (30,400)
                                                                                    ----------      ----------
     Net cash provided by financing activities                                           4,891           8,861
                                                                                    ----------      ----------
 Net increase in cash and cash equivalents                                                 452             295
 Cash and cash equivalents at beginning of period                                          554              88
                                                                                    ==========      ==========
 Cash and cash equivalents at end of period                                         $    1,006      $      383
                                                                                    ==========      ==========

 Supplemental disclosures of cash flow information: 
 Cash paid during the period for:
        Interest                                                                    $      822      $      954
        Income taxes                                                                     4,094           1,577
</TABLE>







              The accompanying notes are an integral part of these
                         condensed financial statements.



                                       5
<PAGE>   6

                 TANDY BRANDS ACCESSORIES, INC. AND SUBSIDIARIES

                     Notes to Condensed Financial Statements
                                   (Unaudited)


Note 1 - Accounting Principles.

         The accompanying unaudited condensed consolidated financial statements
have been prepared in accordance with generally accepted accounting principles
for interim financial information and with the instructions to Form 10-Q and
Article 10 of Regulation S-X. Accordingly, they do not include all of the
information and footnotes required by generally accepted accounting principles
for complete financial statements. In the opinion of management, all adjustments
(consisting of normal recurring accruals) considered necessary for a fair
presentation have been included. Operating results for the three and nine month
periods ended March 31, 1998, are not necessarily indicative of the results that
may be expected for the year ended June 30, 1998. For further information, refer
to the consolidated financial statements and footnotes thereto included in the
Tandy Brands Accessories, Inc. and Subsidiaries Annual Report on Form 10-K for
the year ended June 30, 1997.

Certain fiscal 1997 amounts have been reclassified to conform with the fiscal 
1998 presentation.

Note 2 - Impact of  New Accounting Standards.

         In February 1997, the Financial Accounting Standards Board ("FASB")
issued Statement of Financial Accounting Standards ("SFAS") No. 128, "Earnings
per Share." SFAS No. 128 replaced the previously reported primary and fully
diluted earnings per share with basic and diluted earnings per share. Unlike
primary earnings per share, basic earnings per share excludes any dilutive
effects of options, warrants and convertible securities. Dilutive earnings per
share is very similar to the previously reported fully diluted earnings per
share. All earnings per share amounts for all periods have been presented, and
where necessary, restated to conform to SFAS No. 128 requirements.

         In June 1997, the FASB issued SFAS No. 130, "Reporting Comprehensive
Income", and No. 131, "Disclosures about Segments of an Enterprise and Related
Information." SFAS No. 130 requires that an enterprise report, by major
component and as a single total, the change in its equity during the period from
nonowner sources, and SFAS No. 131 establishes annual and interim reporting
requirements for an enterprise's operating segments and related disclosures
about its products and services, geographical areas in which it operates and
major customers. Both statements are effective for fiscal years beginning after
December 15, 1997, with earlier application permitted. Effects of the adoption
of these statements during fiscal year 1999 will primarily be limited to the
form and content of the Company's disclosures and is not expected to materially
impact the Company's consolidated financial position or statements of
operations, stockholders' equity and cash flows.

Note 3 - Credit Arrangements.

         On March 31, 1998 the Company amended the $25,000,000 unsecured line of
credit with a bank to $30,000,000. Of this amount $20,000,000 is a committed
facility which was scheduled to expire on April 30, 1999 was extended to April
30, 2000. The $5,000,000 uncommitted facility was increased to $10,000,000. Each
facility may be used for borrowings or letters of credit.

Note 4 - Subsequent Events.

         On May 12, 1998, TBAC-AR Acquisition, Inc. ("AR"), a wholly owned
subsidiary of the Company, acquired certain assets of AR Accessories Group, Inc.
through an auction held in the Bankruptcy Court for the Eastern District of
Wisconsin. The assets included, but were not limited to wholesale accounts
receivable, wholesale inventory, certain machinery and equipment, the
distribution center located in West Bend, Wisconsin and related trade names
including "Amity" and "Rolfs". The cash purchase price of approximately
$18,550,000 was provided by drawing on existing bank lines.





                                       6
<PAGE>   7
                 TANDY BRANDS ACCESSORIES, INC. AND SUBSIDIARIES

                     Notes to Condensed Financial Statements
                                   (Unaudited)

Note 5 - Earnings Per Share.

The following sets forth the computation of basic and diluted earnings per share
(in thousands, except per share amounts):

<TABLE>
<CAPTION>
                                                              Three Months                      Nine Months 
                                                                 Ended                            Ended     
                                                                March 31                         March 31   
                                                          ---------------------            ---------------------
                                                           1998          1997               1998          1997
                                                          -------       -------            -------       -------
<S>                                                       <C>           <C>                <C>           <C>
Numerator for basic and diluted earnings per                                    
   share:                                                 $ 1,384       $   745            $ 6,047       $ 3,508
                                                          =======       =======            =======       ======= 
   Net income

Denominator:

         Weighted average shares outstanding                5,569         5,461              5,548         5,432
         Contingently issuable shares                          18             9                 16             5
                                                          -------       -------            -------       -------
    Denominator for basic earnings per
         share - weighted average shares                    5,587         5,470              5,564         5,437

    Effect of dilutive securities:

         Employee stock options                               114            33                 86            25
         Director stock options                                15             3                 16             1
                                                          -------       -------            -------       -------
    Dilutive potential common shares                          129            36                 98            26

    Denominator for diluted earnings per
         share - adjusted weighted - average
         shares                                             5,716         5,506              5,662         5,463
                                                          =======       =======            =======       ======= 

    Basic earnings per share                              $  0.25       $  0.14            $  1.09       $  0.65
                                                          =======       =======            =======       ======= 

    Diluted earnings per share                            $  0.24       $  0.14            $  1.07       $  0.64
                                                          =======       =======            =======       ======= 
</TABLE>



                                       7
<PAGE>   8
                   MANAGEMENT'S DISCUSSION AND ANALYSIS OF
          CONSOLIDATED FINANCIAL CONDITION AND RESULTS OF OPERATIONS
               TANDY BRANDS ACCESSORIES, INC. AND SUBSIDIARIES

GENERAL

Tandy Brands Accessories, Inc. (the "Company") manufactures and markets men's,
women's and children's accessories. The Company's business is conducted
primarily in the United States. Historically, the Company's sales and operating
results are generally consistent throughout the fiscal year, but there is
normally a seasonal increase during the second quarter.

Although the Company's operations are affected by general economic trends, the
Company does not believe that inflation has had a material effect on the results
of operations.

On May 12, 1998, TBAC-AR Acquisition, Inc. ("AR"), a wholly owned subsidiary of
the Company, acquired certain assets of AR Accessories Group, Inc. through an
auction held in the Bankruptcy Court for the Eastern District of Wisconsin. AR
Accessories Group was a manufacturer and distributor of men's and women's small
leather goods. The assets included, but were not limited to wholesale accounts
receivable, wholesale inventory, certain machinery and equipment, the
distribution center located in West Bend, Wisconsin and related trade names
including "Amity" and "Rolfs". The cash purchase price of approximately
$18,550,000 was provided by drawing on existing bank lines.

RESULTS OF OPERATIONS

Three and Nine Months Ended March 31, 1998 Compared to the Three and Nine Months
Ended March 31, 1997

For the three month period ended March 31, 1998, net sales increased 37.8% to
$32,970,000 as compared to net sales of $23,922,000 for the same period last
year. Net income for the third quarter increased 85.8% to $1,384,000 or $.24 per
share, compared to net income of $745,000 or $.14 per share, for the same three
months last year.

For the nine month period ended March 31, 1998, net sales increased 29.9% to
$100,658,000 as compared to net sales of $77,462,000 for the same period last
year. Net income for the nine month period increased 72.4% to $6,047,000 or
$1.07 per share, compared to net income of $3,508,000 or $.64 per share, for the
same nine months last year.

Women's products had net sales increases over the prior year in the comparable
three and nine month periods of $8,287,000 and $20,693,000, respectively. The
women's product net sales for the three-month period of fiscal 1998 were higher
than normal expectations due to increased spring shipments to certain mass
merchants. Women's product net sales for the nine-month period of fiscal 1998
were higher than the same period last year due in part to initial order
shipments of scarves, women's and children's socks, hair goods and Jones New
York(R) handbags to certain key customers in addition to increased women's
accessories sales.

Men's products had net sales increases over the prior year in the comparable
three and nine month periods of $761,000 and $2,503,000, respectively. The men's
products had net sales increases for the three and nine month periods of fiscal
1998 due to increased retail store distribution under the Haggar(R) and Greg
Norman Collection(R) brand names.

For the three and nine month periods gross margins decreased 0.9% and 0.2% to
36.5% and 36.9%, respectively, as compared to the same periods for the prior
year. During the three and nine month periods increases in men's gross margins
offset lower women's product sales gross margins.




                                       8
<PAGE>   9
Selling, general and administrative expenses as a percentage of net sales for
the three and nine months ended March 31, 1998 decreased 2.1% as compared to the
same periods of the prior year. A portion of this decrease resulted from a
larger mix of women's product sales, which, on a percentage of sales basis,
incur lower variable selling expenses than men's product sales. Additionally,
the majority of the sales increases for the three and nine month periods of
fiscal 1998 were to customers on which no sales commissions are paid, which
decreased selling costs as a percentage of sales. Although the Company's
selling, general and administrative expenses were favorably impacted by the
larger mix of women's product sales, the Company anticipates that such expenses
in the future will be in line with historical trends.

The effective tax rate for the nine months ended March 31, 1998 was 38.5%
compared to 37.4% for the same prior year period due to increased state income
taxes.

LIQUIDITY AND CAPITAL RESOURCES

Generally, the Company's primary sources of liquidity are cash flows from
operations and the Company's lines of credit. The Company has two unsecured
domestic bank credit lines aggregating $55,000,000, which can be used for
seasonal borrowings and letters of credit. The Company's borrowings under its
credit lines were $19,700,000 and $22,850,000 as of March 31, 1998 and 1997,
respectively.

See Note 3 for discussion of the amendment to certain credit arrangements.

For the nine months ended March 31, 1998, the Company's operating activities
used cash of $2,955,000 compared to $7,791,000 for the same period last year.
The decrease was attributable to cash receipts collected from the increase in
second quarter of fiscal 1998 sales which were used to fund the purchase of
inventory during the three months ended March 31, 1998.

Capital expenditures were $1,484,000 for the nine months ended March 31, 1998.
The increase of $709,000 over the same prior year period is due primarily to the
purchase of software applications for the Company's management information
systems.

The Company believes that its sources of liquidity are sufficient to fund its
operations.

FORWARD-LOOKING STATEMENTS

This Management's Discussion and Analysis of financial condition and results of
operations and other sections of this Form 10-Q contain forward looking
statements that are based on current expectations, estimates and projections
about the industry in which the Company operates, management's beliefs and
assumptions made by management. In addition, other written or oral statements
which constitute forward-looking statements may be made by or on behalf of the
Company. Words such as "expects," "anticipates," "intends," "plans," "believes,"
"seeks," "estimates," or variations of such words and similar expressions are
intended to identify such forward-looking statements. These statements are not
guarantees of future performance and involve certain risks, uncertainties and
assumptions which are difficult to predict. Therefore, actual outcomes and
results may differ materially from what is expressed or forecasted in such
forward-looking statements. The Company undertakes no obligation to update
publicly any forward-looking statements, whether as a result of new information,
future events or otherwise.




                                       9
<PAGE>   10


                 TANDY BRANDS ACCESSORIES, INC. AND SUBSIDIARIES
                           PART II - OTHER INFORMATION



ITEM 6.  Exhibits and Reports on Form 8-K.

         No reports on Form 8-K were filed during the quarter ended March 31,
1998. The exhibits filed as a part of this report are listed below.


                  Exhibit No.               Description

                    10                      Material Contracts

                    27                      Financial Data Schedules


                                       10
<PAGE>   11
                 TANDY BRANDS ACCESSORIES, INC. AND SUBSIDIARIES

                                   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.


                                TANDY BRANDS ACCESSORIES, INC.
                                (Registrant)




                                /s/ J.S.B. Jenkins
                                ----------------------------------------------
                                J.S.B. Jenkins
                                President and Chief Executive Officer





                                /s/ Stanley T. Ninemire
                                ----------------------------------------------
                                Stanley T. Ninemire
                                Senior Vice President, Chief Financial Officer
                                and Treasurer



Date: May 13, 1998





                                       11
<PAGE>   12



                 TANDY BRANDS ACCESSORIES, INC. AND SUBSIDIARIES
                                  EXHIBIT INDEX




<TABLE>
<CAPTION>
                                                           Incorporated by Reference
                                                                (If applicable)
                                             -------------------------------------------------------
Exhibit Number and Description                 Form          Date           File No.       Exhibit
                                             ---------    ------------     -----------    ----------
<S>                                          <C>          <C>              <C>            <C> 
(4)   Instruments defining the rights
      of security holders, including
      indentures

      4.1  Certificate of Designations,
           Powers, Preferences and
           Rights of Series A Junior
           Participating Cumulative
           Preferred Stock of Tandy
           Brands Accessories, Inc.            S-1        11/02/90         33-37588          4.1

      4.2  Form of Common Stock
           Certificate of Tandy
           Brands Accessories, Inc.            S-1        11/02/90         33-37588          4.2

      4.3  Form of Preferred Share
           Purchase Rights Certificate
           of Tandy Brands
           Accessories, Inc.                   S-1        11/02/90         33-37588          4.3

      4.4  Rights Agreement dated
           November 7, 1990,
           between Tandy Brands
           Accessories, Inc.
           and First National
           Bank of Boston                      S-1        11/02/90         33-37588         10.5

(10)  Material Contracts

10.23 Amendments No. 4 and 5
      to the Credit Agreement
      between Tandy Brands
      Accessories, Inc. and Chase
      Bank (Texas Commerce)
      of  Texas dated June 30, 1994            N/A            N/A             N/A            N/A

(27)  Financial Data Schedule

27.1  Financial Data Schedule                  N/A            N/A             N/A            N/A

27.2  Financial Data Schedule                  N/A            N/A             N/A            N/A

27.3  Financial Data Schedule                  N/A            N/A             N/A            N/A

27.4  Financial Data Schedule                  N/A            N/A             N/A            N/A

27.5  Financial Data Schedule                  N/A            N/A             N/A            N/A
</TABLE>




                                       12