<PAGE>   1
                                  UNITED STATES
                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549

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

                                   FORM 10-K/A

(Mark One)
[X]      ANNUAL REPORT PURSUANT TO SECTION 13 or 15(d) OF THE SECURITIES
         EXCHANGE ACT OF 1934

                    For the fiscal year ended June 30, 1998.
                                       or
[   ]    TRANSITION REPORT PURSUANT TO SECTION 13 or 15(d) OF THE SECURITIES
         EXCHANGE ACT OF 1934

                For the transition period from          to .

                         Commission File Number 1-13521

                              HYPERCOM CORPORATION
             (Exact name of registrant as specified in its charter)

<TABLE>
<S>                                         <C>
           DELAWARE                                       86-0828608
(State or other jurisdiction of             (I.R.S. Employer Identification No.)
 incorporation or organization)
</TABLE>

                             2851 West Kathleen Road
                             Phoenix, Arizona 85053
               (Address of principal executive offices) (Zip Code)
                                 (602) 504-5000
              (Registrant's telephone number, including area code)

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

<TABLE>
<S>                                    <C>
       Title of Class                  Name of each Exchange on which registered
COMMON STOCK, $.001 PAR VALUE                   NEW YORK STOCK EXCHANGE
</TABLE>

        Securities registered pursuant to Section 12(g) of the Act: None

         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 by check mark if disclosure of delinquent filers pursuant to
Item 405 of Regulation S-K is not contained herein, and will not be contained,
to the best of registrant's knowledge, in definitive proxy or information
statements incorporated by reference in Part III of this Form 10-K or any
amendment to this Form 10-K. [ ]

         At September 22, 1998, the aggregate market value of voting stock held
by non-affiliates of the Registrant was $65,573,058 based on the closing market
price of the Common Stock on such date, as reported by the New York Stock
Exchange.

         Indicate the number of shares outstanding of each of the registrant's
classes of common stock, as of the latest practicable date: 33,594,166 shares of
the Registrant's Common Stock were outstanding as of September 22, 1998.

                       DOCUMENTS INCORPORATED BY REFERENCE

         Material from the Registrant's Proxy Statement relating to its 1998
Annual Meeting of Shareholders have been incorporated by reference into Part
III, Items 10, 11, 12, and 13.
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EXPLANATORY NOTE: This Form 10-K/A amends the Registrant's Form 10-K originally
filed on September 28, 1998 (the "Original Filing"). Item 14(c) and the Exhibit
Index, which are set forth in their entirety on page 2 and 4 respectively, are
amended by adding reference to Exhibits 10.1 - 10.12. All exhibits listed in
Item 14(c) and the Exhibit Index are either hereby incorporated by reference
from a previously filed registration statement, filed with the Original Filing,
or filed herein with this Form 10-K/A. Any items in the Original Filing not
expressly changed hereby shall be as set forth in the Original Filing.


                                     PART IV

Item 14.          EXHIBITS, FINANCIAL STATEMENT SCHEDULES, AND REPORTS ON
                  FORM 8-K

(c)

<TABLE>
<CAPTION>
Exhibit No.       Exhibit Description

<S>               <C>
3.1*              Amended and Restated Certificate of Incorporation of the
                  Company. Incorporated by reference to Exhibit 3.1 of the
                  Company's Form S-1 Registration Statement Under The Securities
                  Act Of 1933.

3.2*              Amended and Restated Bylaws of the Company. Incorporated by
                  reference to Exhibit 3.2 of the Company's Form S-1
                  Registration Statement Under The Securities Act of 1933.

4*                Amended and Restated Certificate of Incorporation of the
                  Company. Incorporated by reference to Exhibit 3.1 of the
                  Company's Form S-1 Registration Statement Under The Securities
                  Act Of 1933.

10.1              Revolving Credit Agreement by and between Hypercom Corporation
                  and Bank One, Arizona, NA, dated January 20, 1998

10.2*             Lease, as amended, dated June 14, 1996, by and between
                  Estes-Samuelson Partnership and Hypercom, Inc.

10.3*             Hypercom Corporation Long-Term Incentive Plan+

10.4*             Hypercom Corporation 1997 Employee Stock Purchase Plan+

10.5*             Promissory Note, dated October 17, 1994, by and between
                  Hypercom, Inc., and George Wallner+

10.6*             Hypercom Corporation Nonemployee Directors' Stock Option Plan+

10.7*             Employment Agreement with Jairo Gonzalez, dated January 1,
                  1997+

10.8*             Employment Agreement with Albert A. Irato, dated January 1,
                  1997+

10.9*             Loan Agreement, dated October 12, 1996, by and between
                  Hypercom Pty. Ltd., and George Wallner+

10.10*            Loan Agreement, dated October 12, 1996, by and between
                  Hypercom Pty. Ltd., and Paul Wallner+

10.11*            Promissory Note, dated December 31, 1994, by and between
                  Hypercom, Inc., and Albert Irato+

10.12*            Description of lease by and between Hypercom Pty. Ltd., and
                  Hypercom Unit Trust

21**              Subsidiaries of the Company

23**              Consent of Independent Public Accountants

27**              Financial Data Schedule
</TABLE>

         * Incorporated by reference to the Registrant's Registration Statement
         on Form S-1 (Registration no. 333-35641), effective November 13, 1997

         ** Filed with the Original Filing

         + Management or Compensatory Plan Agreement


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<PAGE>   3
                                   SIGNATURES

         Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, the registrant has duly caused this report on Form 10-K/A
to be signed on its behalf by the undersigned, thereunto duly authorized.

                                                HYPERCOM CORPORATION,
                                                a Delaware corporation


                                      By: /s/ Albert A. Irato
                                          -------------------------------------
                                          Albert A. Irato
                                          President and Chief Executive Officer

                                      Date: November 3, 1998


      Pursuant to the requirements of the Securities Exchange Act of 1934, this
report on Form 10-K/A has been signed below by the following persons on behalf
of the registrant and in the capacities and on the dates indicated.

<TABLE>
<CAPTION>
                Name and Signature                                  Title                          Date
                ------------------                                  -----                          ----

<S>                                                  <C>                                  <C>
 /s/ Albert A. Irato                                 President, Chief Executive           November 3, 1998
---------------------------------------------------  Officer and Director (Principal
Albert A. Irato                                      Executive Officer)




 /s/ Thomas E. Linnen                                Chief Financial Officer and          November 3, 1998
---------------------------------------------------  Director (Principal Financial
Thomas E. Linnen                                     and Accounting Officer)





/s/ George Wallner                                   Chairman of the Board of             November 3, 1998
---------------------------------------------------  Directors
George Wallner


/s/ Paul Wallner                                     Director                             November 3, 1998
---------------------------------------------------
Paul Wallner


/s/ Jario Gonzalez                                   Director                             November 3,  1998
---------------------------------------------------
Jario Gonzalez


/s/ William E. Fisher                                Director                             November 3, 1998
---------------------------------------------------
William E. Fisher



/s/ Peter J. Hart                                    Director                             November 3, 1998
---------------------------------------------------
Peter J. Hart
</TABLE>

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<PAGE>   4
LIST OF EXHIBITS

<TABLE>
<CAPTION>
Exhibit No.           Exhibit Description

<S>               <C>
3.1*              Amended and Restated Certificate of Incorporation of the
                  Company. Incorporated by reference to Exhibit 3.1 of the
                  Company's Form S-1 Registration Statement Under The Securities
                  Act Of 1933.

3.2*              Amended and Restated Bylaws of the Company. Incorporated by
                  reference to Exhibit 3.2 of the Company's Form S-1
                  Registration Statement Under The Securities Act of 1933.

4*                Amended and Restated Certificate of Incorporation of the
                  Company. Incorporated by reference to Exhibit 3.1 of the
                  Company's Form S-1 Registration Statement Under The Securities
                  Act Of 1933.

10.1              Revolving Credit Agreement, by and between Hypercom
                  Corporation, and Bank One, Arizona, NA, dated January 20,
                  1998+

10.2*             Lease, as amended, dated June 14, 1996, by and between
                  Estes-Samuelson Partnership and Hypercom, Inc.

10.3*             Hypercom Corporation Long-Term Incentive Plan+

10.4*             Hypercom Corporation 1997 Employee Stock Purchase Plan+

10.5*             Promissory Note, dated October 17, 1994, by and between
                  Hypercom, Inc., and George Wallner+

10.6*             Hypercom Corporation Nonemployee Directors' Stock Option Plan+

10.7*             Employment Agreement with Jairo Gonzalez, dated January 1,
                  1997+

10.8*             Employment Agreement with Albert A. Irato, dated January 1,
                  1997+

10.9*             Loan Agreement, dated October 12, 1996, by and between
                  Hypercom Pty. Ltd., and George Wallner+

10.10*            Loan Agreement, dated October 12, 1996, by and between
                  Hypercom Pty. Ltd., and Paul Wallner+

10.11*            Promissory Note, dated December 31, 1994, by and between
                  Hypercom, Inc., and Albert Irato+

10.12*            Description of lease by and between Hypercom Pty. Ltd., and
                  Hypercom Unit Trust

21**              Subsidiaries of the Company

23**              Consent of Independent Public Accountants

27**              Financial Data Schedule
</TABLE>

         * Incorporated by reference to the Registrant's Registration Statement
         on Form S-1 (Registration no. 333-35641), effective November 13, 1997

         ** Filed with the Original Filing

         + Management or Compensatory Plan Agreement


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