<PAGE>   1

================================================================================

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                   FORM 10-K/A

[X]  Amendment No. 1 to Annual Report pursuant to Section 13 or 15(d) of the
     Securities Exchange Act of 1934 for the fiscal year ended September 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 NO. 1-10459

                              GENEVA STEEL COMPANY
               (Exact name of Registrant as specified in charter)


<TABLE>
<CAPTION>
                UTAH                                               93-0942346
<S>                                                    <C>
     (State or other jurisdiction                      (I.R.S. Employer Identification No.)
   of incorporation or organization)
        10 SOUTH GENEVA ROAD
           VINEYARD, UTAH                                             84058
 (Address of principal executive office)                             (Zip Code)
</TABLE>

       Registrant's telephone number, including area code: (801) 227-9000

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


<TABLE>
<CAPTION>
                                                              Name of Each Exchange on
        Title of Each Class                                      Which Registered
<S>                                                           <C>
       CLASS A COMMON STOCK,                                  
           NO PAR VALUE                                        
       WARRANTS TO PURCHASE
       CLASS A COMMON STOCK                                   
</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. [X]

         The aggregate market value of the Class A Common Stock held by
non-affiliates of the Registrant, based upon the closing sale price of the Class
A Common Stock on the New York Stock Exchange per share on January 19, 1999, was
approximately $7,441,955. Shares of Class A Common Stock held by each officer
and director and by each person who may be deemed to be an affiliate have been
excluded. As of January 19, 1999, the Registrant had 14,975,265 and 18,451,348
shares of Class A and Class B Common Stock, respectively, outstanding.



================================================================================

<PAGE>   2

                                 AMENDMENT NO. 1

         The Registrant hereby amends its Annual Report on Form 10-K for the
fiscal year ended September 30, 1998, previously filed with the Commission (the
"Annual Report") solely for the purpose of including Part III, Items 10 through
13, as a part of this report on Form 10-K.

                                    PART III

ITEM 10.   DIRECTORS AND EXECUTIVE OFFICERS OF THE REGISTRANT.

         The following table sets forth information with respect to the
executive officers and directors of the Company:


<TABLE>
<CAPTION>
NAME                                       AGE       POSITION
----                                       ---       --------
<S>                                        <C>       <C>
Joseph A. Cannon.......................    49        Chairman of the Board and Chief Executive Officer
Ken C. Johnsen.........................    40        Executive Vice President, General Counsel and Director
Dennis L. Wanlass......................    49        Vice President, Treasurer and Chief Financial Officer
Tim Clark..............................    34        Vice President of Manufacturing
Carl E. Ramnitz........................    51        Vice President of Human Resources
Robert J. Grow.........................    49        Director
R. J. Shopf............................    64        Director
Alan C. Ashton.........................    55        Director
K. Fred Skousen........................    56        Director
Kevin S. Flannery......................    54        Director
Gregory T. Hradsky.....................    38        Director
</TABLE>

         The following sets forth the background of each of the Company's
executive officers and directors, including the principal occupation of those
individuals for the past five years:

         JOSEPH A. CANNON has been a director of the Company since its inception
in February 1987, and has served as Chairman of the Board of Directors from
March 1987 to the present. Mr. Cannon served as President of the Company from
July 1987 to May 1991 and as Chief Executive Officer from July 1987 to July
1991. Following an absence from July 1991 to October 1992, Mr. Cannon returned
to the Company as Chief Executive Officer and has continued to serve in such
capacity. From February 1985 to September 1987, Mr. Cannon was engaged in the
private practice of law with Pillsbury, Madison & Sutro in its Washington, D.C.
office, specializing in environmental law. From May 1981 to February 1985, he
was employed in various capacities by and became Assistant Administrator of the
Environmental Protection Agency. As Assistant Administrator, Mr. Cannon was
responsible for the development, implementation and enforcement of federal air
quality and radiation regulations throughout the United States.

         KEN C. JOHNSEN has been Executive Vice President and General Counsel of
the Company since November 1997 and has served as Secretary of the Company since
February 1992. He served as Vice President and General Counsel from November
1991 to November 1997 and as Manager of Special Projects for the Company from
February 1991 through October 1991. From 1986 to 1991, Mr. Johnsen was engaged
in the private practice of law with Parr Waddoups Brown Gee & Loveless,
specializing in corporate counseling and civil litigation. Mr. Johnsen received
his law degree from Yale Law School and a B.A. degree in Finance from Utah State
University.

         DENNIS L. WANLASS has been Vice President, Treasurer and Chief
Financial Officer of the Company since September 1989 and was Controller of the
Company from January 1988 to September 1989. Before joining the Company, Mr.
Wanlass was employed by Eastman Christensen, then a joint venture of Norton
Company and Texas Eastern, in various accounting and financial capacities. From
1970 to 1975, he was employed by KPMG, an international accounting and
consulting firm. Mr. Wanlass has a B.S. in Accounting from the University of
Utah and is a certified public accountant.

         TIM CLARK has been Vice President of Manufacturing since May 1997. He
has been employed by the Company since 1993 in several positions, including
Project Manager--Plate Finishing and Shipping, Director of Corporate



                                       1
<PAGE>   3

Communications, Director--Delta Project and Assistant to the President. Mr.
Clark obtained B.A. and M.A. degrees from Brigham Young University and the
University of Utah in 1988 and 1993, respectively.

         CARL E. RAMNITZ has been Vice President of Human Resources since
October 1988 and was Vice President of Human Resources and Public Affairs of the
Company from September 1987 to September 1988. Prior to joining the Company, he
was employed by USX for 18 years in various employment and labor related
capacities, most recently as Manager of Employee Relations for the Geneva Steel
plant before it was acquired by the Company and for USX's Pittsburgh, California
steel plant.

         ROBERT J. GROW served as President of the Company from May 1991 to
January 1999 and served as Chief Operating Officer from December 1989 until
December, 1998. Mr. Grow was elected 1996 Chairman of the American Iron & Steel
Institute ("AISI"). AISI is the premier industry association for steel companies
in the United States, Canada and Mexico. From August 1988 to December 1989, he
was employed by the Company in various capacities, including Vice President,
Executive Vice President and General Counsel. He has served as a director of the
Company from its inception. From 1976 to September 1987, Mr. Grow was engaged in
the private practice of law with the Salt Lake City, Utah law firm of Parr
Waddoups Brown Gee & Loveless, specializing in real property and general
corporate law. Mr. Grow also holds a B.S. degree in Electrical Engineering from
the University of Utah.

         R. J. SHOPF has been a director of the Company since September 1989 and
served as an independent advisor to the Company from March 1988 to September
1989. Mr. Shopf currently serves as the Chairman of the Board for companies
which own and operate two Ruth's Chris Steak Houses and the Montgomery Inn
Restaurant in Indianapolis. He is also the President of Southwest Business
Associates, a consulting company (a position which he previously held from 1984
to February 1988, and from January 1989 to October 1992), and has served in this
capacity since August 1994. Mr. Shopf served as President and Chief Executive
Officer of Pioneer Chlor Alkali, Inc. ("Pioneer") from August 1993 until August
1994. Mr. Shopf also served as President of Imperial West Chemical Company, an
affiliate of Pioneer, from January 1992 until August 1994, and as President of
All Pure Chemical Company, also an affiliate of Pioneer, from October 1992 until
August 1994. Mr. Shopf obtained an MBA degree from the Harvard Graduate School
of Business Administration in 1959.

         ALAN C. ASHTON has been a director of the Company since November 1996.
Dr. Ashton co-founded the former WordPerfect Corporation ("WordPerfect"), a
software applications company. Dr. Ashton served as an executive officer and a
director of WordPerfect and its subsidiaries for over five years, including as
Co-Chairman of the Board of Directors of WordPerfect from January through June
1994, and as President and Chief Executive Officer of WordPerfect from January
1993 through December 1993. He served as a director of Novell, Inc. from June
1994 until he resigned in December 1996. Dr. Ashton and his wife, Karen, are
co-founders of Thanksgiving Point in Lehi, Utah. He is currently serving on the
Board of Directors for Infobases, Bookcraft, Brigham Young University's Lighting
the Way Campaign, and the Division of Business and Economic Development.

         K. FRED SKOUSEN is currently Advancement Vice President of Brigham
Young University. Formerly, he was the Dean of the Marriott School of Management
at BYU for nine years. Prior to that, Dr. Skousen held the Peat Marwick Mitchell
Professorship and, from 1974 to 1983, served as Director of the School of
Accountancy at BYU. Dr. Skousen is a certified public accountant.

         KEVIN S. FLANNERY has been, since 1993, President of Whelan Financial
Corp., a New York company engaged in management of investments. He previously
served as Senior Managing Director of Bear Stearns, an investment banking firm,
for 16 years.

         GREGORY T. HRADSKY is the President of Bellport Capital Corp., a
private investment company, which was founded in May 1998. Mr. Hradsky was
Managing Director of UBS Securities LLC, a New York based investment banking
firm from 1991 to 1998. Prior to that, Mr. Hradsky was a member of the
Distressed Securities Group and High Yield Research Department at The First
Boston Corporation from 1988 to 1991. He began his career at T. Rowe Price
Associates in 1983. Mr. Hradsky received a MBA in Finance from the Wharton
School in 1988 and a BA from Loyola College in 1982.




                                       2
<PAGE>   4

SECTION 16(a) BENEFICIAL OWNERSHIP REPORTING COMPLIANCE

         Section 16(a) of the Exchange Act requires the Company's executive
officers and directors to file initial reports of ownership and reports of
changes in ownership with the SEC and the New York and Pacific Stock Exchanges.
Executive officers and directors are required by SEC regulations to furnish the
Company with copies of all Section 16(a) forms they file. Based solely on a
review of the copies of such forms furnished to the Company and written
representations from the Company's executive officers and directors, the Company
noted that all required forms were timely filed during the past fiscal year.



                                       3
<PAGE>   5

ITEM 11.   EXECUTIVE COMPENSATION.

         The compensation of Joseph A. Cannon, the Company's Chief Executive
Officer, and the four other most highly paid executive officers (collectively,
the "Named Executive Officers") is discussed in the following tables and in a
report from the Compensation Committee of the Board of Directors.


SUMMARY COMPENSATION TABLE

         The following table sets forth, for the fiscal years ended September
30, 1998, 1997 and 1996, the compensation paid to the Company's Named Executive
Officers.

<TABLE>
<CAPTION>
                                                                                               LONG-TERM COMPENSATION
                                                                                 ---------------------------------------------------
                                             ANNUAL COMPENSATION                          AWARDS                    PAYOUTS
                               ------------------------------------------------  -------------------------  ------------------------
                                                                                 RESTRICTED    SECURITIES               
                                                                  OTHER ANNUAL     STOCK       UNDERLYING     LTIP       ALL OTHER
          NAME AND                        SALARY        BONUS     COMPENSATION    AWARD(S)      OPTIONS     PAYOUTS    COMPENSATION
     PRINCIPAL POSITION         YEAR      ($)(1)       ($)(2)          ($)         ($)(3)        (#)(4)       ($)        ($)(5)
-----------------------------  -------  -----------  -----------  -------------  ----------   ------------  --------   -------------
<S>                            <C>      <C>          <C>          <C>            <C>          <C>           <C>        <C>   
Joseph A. Cannon                1998      487,724         44,201     12,430          0              68,771      0         17,980
Chief Executive                 1997      463,337         50,932     13,858          0             100,000      0         16,726
Officer                         1996      487,964         54,791     12,924          0              12,000      0         17,390
                                                                                
Robert J. Grow                  1998      434,985         39,421     12,430          0              58,497      0         17,980
President                       1997      413,236         45,425     13,858          0             123,000      0         16,726
                                1996      435,200         48,867     12,924          0              11,000      0         17,390
                                                                                
Richard D. Clayton              1998      291,759         26,441     12,430          0              39,175      0         16,878
Senior Vice President of        1997      277,171         30,468     13,858          0             109,500      0         17,362
Marketing and Distribution      1996      291,902         32,776     12,924          0               9,000      0         16,199
                                                                                
Ken C. Johnsen                  1998      275,010         24,455      8,859          0              31,589      0         16,724
Executive Vice President        1997      200,220         21,886      9,073          0              50,000      0         14,021
and General Counsel             1996      195,083         22,050      9,307          0               9,000      0         17,077
                                                                                
Dennis L. Wanlass               1998      196,275         17,788      5,757          0              29,627      0         17,837
Vice President and              1997      186,461         20,497      9,073          0              84,500      0         15,650
Chief Financial Officer         1996      196,371         22,050      9,827          0               7,000      0         18,190
                                                                            
</TABLE>

----------
(1)      Includes compensation deferred or accrued at the election of the Named
         Executive Officer under the Company's Management Employee Savings and
         Pension Plan (the "Management Plan").
(2)      Represents payments under the Company's Performance Dividend Plan in
         such years. Amounts for all three years represent only Performance
         Dividend Payments payable to all management and union employees based
         upon the Company's volume of product shipments.
(3)      None of the Named Executive Officers received any restricted stock
         awards during the three years presented, nor did any of them hold any
         such stock as of September 30, 1998.
(4)      1997 option grants represent new options granted on February 20, 1997
         and the repricing on March 26, 1997 of options granted to the Named
         Executive Officers in fiscal year 1991. The number of replacement
         options reflected as 1997 grants are as follows: Robert J. Grow,
         33,000; Richard D. Clayton, 49,500 and Dennis L. Wanlass, 39,500.
(5)      Includes contributions made by the Company pursuant to the Management
         Plan and the dollar value of premiums paid by the Company pursuant to
         the Company's split dollar life insurance plan. For fiscal year 1998,
         such amounts were as follows: Joseph A. Cannon, $14,400 Company
         contributions, $3,580 insurance premiums; Robert J. Grow, $14,400
         Company contributions, $3,580 insurance premiums; Richard D. Clayton,
         $14,400 Company contributions, $2,478 insurance premiums; Ken C.
         Johnsen, $14,400 Company contributions, $2,324 insurance premiums and
         Dennis L. Wanlass, $14,400 Company contributions, $3,437 insurance
         premiums.



                                       4
<PAGE>   6

OPTION GRANTS IN LAST FISCAL YEAR

         The following table sets forth information with respect to individual
grants of stock options made by the Company to the Named Executive Officers
during the fiscal year ended September 30, 1998. The Company did not grant any
stock appreciation rights during the fiscal year ended September 30, 1998.


<TABLE>
<CAPTION>
                                                                                                     POTENTIAL REALIZABLE VALUE
                                                                                                     AT ASSUMED ANNUAL RATES OF 
                                                                                                     STOCK  PRICE APPRECIATION
                                                    INDIVIDUAL GRANTS                                     FOR OPTION TERM
                               ------------------------------------------------------------------    -------------------------
                                                    PERCENT OF
                                  NUMBER OF        TOTAL OPTIONS
                                  SECURITIES        GRANTED TO         EXERCISE OR
                                  UNDERLYING       EMPLOYEES IN         BASE PRICE    EXPIRATION
         NAME                  OPTIONS GRANTED(#)   FISCAL YEAR         ($/SH)(3)         DATE            5%($)       10%($)
         ----                  ------------------   -----------         ---------         ----            -----       ------
<S>                            <C>                 <C>                 <C>            <C>                 <C>         <C>
Joseph A. Cannon                    48,771(1)          16.6%               $3.000      12/19/07            --           --
                                    20,000(2)           6.8                 2.438      02/24/08            --           --
                                                                          
Robert J. Grow(4)                   43,497(1)          14.8                 3.000      12/19/07            --           --
                                    15,000(2)           5.1                 2.438      02/24/08            --           --
                                                                          
Richard D. Clayton(4)               29,175(1)          10.0                 3.000      12/19/07            --           --
                                    10,000(2)           3.4                 2.438      02/24/08            --           --
                                                                          
Ken C. Johnsen                      21,589(1)           7.3                 3.000      12/19/07            --           --
                                    10,000(2)           3.4                 2.438      02/24/08            --           --
                                                                          
Dennis L. Wanlass                   19,627(1)           6.7                 3.000      12/19/07            --           --
                                    10,000(2)           3.4                 2.438      02/24/08            --           --
</TABLE>

(1)      The market price of the underlying Class A Common Stock on the date of
         grant was $2.438 per share on December 19, 1997 and $2.063 per share on
         February 24, 1998, respectively.

(2)      Fifty percent of the options granted to the Named Executive Officers on
         February 24, 1998 became exercisable on February 24, 1999 and the
         balance become exercisable on February 24, 2000.

(3)      The options granted on December 19, 1997 become immediately exercisable
         in full on next business day following the tenth consecutive trading
         day that the per share closing sales price of the Class A Common Stock,
         as reported on the NYSE, is $5.00 or greater.

(4)      Richard D. Clayton and Robert J. Grow resigned from the Company on
         December 31, 1998 and January 21, 1999, respectively.



                                       5
<PAGE>   7

AGGREGATED OPTION EXERCISES IN LAST FISCAL YEAR AND FISCAL YEAR-END OPTION
VALUES

         The following table sets forth information with respect to the exercise
of options to acquire shares of the Company's Class A Common Stock by the Named
Executive Officers during the fiscal year ended September 30, 1998, as well as
the aggregate number and value of unexercised options held by the Named
Executive Officers on September 30, 1998.

<TABLE>
<CAPTION>
                                                      NUMBER OF SECURITIES UNDERLYING     VALUE OF UNEXERCISED
                                                           UNEXERCISED OPTIONS           IN-THE-MONEY OPTIONS AT
                                                         AT SEPTEMBER 30, 1998(#)         SEPTEMBER 30, 1998($)
                        SHARES ACQUIRED     VALUE      ----------------------------    ----------------------------
        NAME            ON EXERCISE (#)  REALIZED ($)  EXERCISABLE    UNEXERCISABLE    EXERCISABLE    UNEXERCISABLE
        ----            ---------------  ------------  -----------    -------------    -----------    -------------
<S>                     <C>              <C>           <C>            <C>              <C>            <C>   
Joseph A. Cannon               0              0           74,000        130,771        $    --          $   --
Robert J. Grow                 0              0          100,000        114,497             --              --
Richard D. Clayton             0              0          112,700         79,975             --              --
Ken C. Johnsen                 0              0           82,400         66,189             --              --
Dennis L. Wanlass              0              0           88,600         60,527             --              --
</TABLE>


DIRECTOR COMPENSATION

         Directors who are not employees of the Company are paid a director's
fee of $22,000 per year for serving on the Board of Directors, $3,000 per year
for serving as chairman of any committee, $1,500 for each Board meeting
attended, $750 for each telephonic board meeting, and $1,000 for each committee
meeting attended. Directors may also receive a fee of between $750 and $1,000
per day for other significant service to the Company. Mr. Shopf serves as
outside "lead" director for which he receives an additional $12,000 per year.
All directors are also reimbursed by the Company for their out-of-pocket travel
and related expenses incurred in attending all Board and committee meetings.

         Under the Geneva Steel Company 1996 Incentive Plan (the "Incentive
Plan"), each nonemployee director is granted an option to purchase 4,000 shares
of the Company's Class A Common Stock upon appointment or election and each
nonemployee director who is serving on the first business day on or after
January 1 of each calendar year is granted an option to purchase 2,000 shares.
Options are exercisable for ten years at the fair market value of the shares on
the date of grant and are subject to a vesting schedule.

         In addition, each nonemployee director who serves for not less than
five years receives a deferred compensation payment in each of the five years
after termination of service in the amount of the retainer paid to such director
for services as a director during the year preceding termination of such
services. If a nonemployee director's service is terminated prior to five years
of service by reason of death or disability, deferred compensation is paid for a
period equal to the period for which the director served.


COMPENSATION COMMITTEE REPORT

         This Report of the Compensation Committee (the "Committee") of the
Board of Directors describes the overall compensation goals and policies
applicable to the executive officers of Geneva, including the bases for
determination of the compensation of executive officers for fiscal year 1998.
The Report also discusses the setting of 1998 compensation of Mr. Cannon. The
term "Executive Officers" is used below to refer to the executive officers of
Geneva other than Mr. Cannon.

         Composition and Functions of the Committee. The Compensation Committee
of the Board of Directors of Geneva is comprised entirely of independent,
nonemployee directors. Subject to any action which may be taken by the full
Board of Directors, the Board has delegated to the Committee the authority:



                                       6
<PAGE>   8

         - To determine the compensation of Joseph A. Cannon, Chairman of the
Board and Chief Executive Officer of Geneva, including discretionary bonuses;

         - To approve, upon recommendations by Mr. Cannon, the compensation
arrangements of Executive Officers of Geneva, including the Named Executive
Officers identified in the Summary Compensation Table above; and

         - To carry out the duties and responsibilities of the Board of
Directors regarding Geneva's other compensation plans, including administering
and making awards under Geneva's option plans to Mr. Cannon, the Executive
Officers and other managers and key employees of Geneva.

         Compensation Philosophy and Objectives. The Committee believes that
compensation of Geneva's executive officers should be set at a competitive level
and be based upon the Company's overall financial performance, achievement of
strategic goals, and individual performance, with a view toward increasing value
of the Company. Within this overall philosophy, the following principles guide
Geneva's compensation policies for executive officers:

         - Provide competitive levels of compensation that enable Geneva to
attract and retain experienced, talented executive officers;

         - Compensate executive officers based on the Company's progress toward
achievement of its short and long-term strategic and financial goals;

         - Compensate executive officers based on the performance of the
individual executive officer, and his contribution to the Company's performance;
and

         - Maintain and strengthen the incentive for executive officers to
increase the value of the Company.

The Committee believes that adherence to these objectives is essential to
attracting and retaining highly-qualified officers whose contributions are
necessary for the growth and success of Geneva. Information concerning the
specific implementation of these policies in the 1998 compensation arrangements
of the Executive Officers and Mr. Cannon is provided below. The Committee
believes that the $1.0 million compensation deduction cap recently promulgated
under the Internal Revenue Code currently has no effect on the Company's
compensation policies.

         Annual Salaries. Salaries of Executive Officers are generally reviewed
on an annual basis at the end of the fiscal year and adjustments made based on
the Committee's subjective evaluation of the individual's performance and the
Company's performance, taking into account both qualitative and quantitative
factors. Among the factors considered by the Committee have been the
recommendations of Mr. Cannon and the importance of retaining key Executive
Officers. Subject to Board approval, the Committee makes compensation decisions
concerning the Executive Officers. Salary levels for fiscal year 1998 were
generally not increased because, in the Committee's judgment, the Company's
operating performance did not warrant increases. Except in the case of three
Executive Officers who recently undertook significantly greater management
responsibilities, there were no increases in base compensation of Executive
Officers. During the year, the Committee did, however, restore a previous salary
reduction taken voluntarily by the Executive Officers and Mr. Cannon. The
Compensation Committee has also relied on compensation surveys of executives
with comparable responsibilities at peer companies. These surveys have been
prepared at periodic intervals by the compensation consulting firm of William E.
Mercer.

         Incentive Bonuses. In fiscal 1998, Geneva continued to make awards
under the Performance Dividend Plan (the "Performance Plan") established in June
1993, which provides for the monthly payment of additional cash compensation as
a percentage of base compensation to all management employees based upon the
Company's product shipments. Cash payments made to Executive Officers under the
Performance Plan during fiscal 1998 were determined according to the same
formula used to determine payments to all other management employees. No
discretionary bonuses were paid to any Executive Officers.

         Stock Options. The Company's Incentive Plan and Key Employee Plan
permit the award of options to purchase Class A Common Stock to executive
officers, managers and key employees. The award of stock options is intended to
align the interests of Executive Officers with the shareholders by providing the
Executive Officers with an incentive to bring about increases in the price of
Class A Common Stock. Geneva's general policy is to award options to purchase



                                       7
<PAGE>   9

Class A Common Stock at a price that equals or exceeds market price on the date
of grant. Accordingly, the Executive Officers derive a financial benefit from an
option only if the price of Class A Common Stock increases. With one exception,
options grants have not had performance contingencies, but realization of the
value provided through the options has generally required the Executive Officer
to remain employed by Geneva until the options vest. Historically, options have
vested at the rate of 40 percent of the underlying shares at the end of two
years following the grant and an additional 20 percent each year thereafter. The
Committee modified the vesting schedule of options granted in fiscal 1997 and
1998 so that 50 percent become vested after one year and the balance after two
years. The modification to the vesting schedule was made in recognition of the
historical volatility of the Company's Common Stock and a desire to increase the
incentive represented by the grant of stock options to Executive Officers. The
options are generally exercisable for ten years from the date of grant at a
price equal to 100 percent of the fair market value of the underlying shares on
such date. Because each of Messrs. Cannon and Grow beneficially own more than 10
percent of the voting power of the Company, applicable tax laws require that
incentive stock options granted to them must be exercisable for no more than
five years at a price equal to the 110 percent of the fair market value on the
date of grant.

         In fiscal 1998, the Company awarded 294,486 options to purchase Class A
Common Stock to Executive Officers of the Company. The number of options awarded
to Executive Officers was based upon the Committee's desire to maintain and
strengthen the incentive for Executive Officers to increase the price of the
Class A Common Stock.

         Compensation of Chief Executive Officer. For the reasons discussed
above with respect to the Executive Officers, there was no increase in Mr.
Cannon's base salary in fiscal 1998, other than the restoration of a previous
voluntary salary reduction. During the 1998 fiscal year, Mr. Cannon received
additional compensation of $44,201, pursuant to the Performance Plan, based upon
the formula applicable to 911 Executive Officers and management employees. Mr.
Cannon was also granted options for the purchase of 68,771 shares of Class A
Common Stock for the reasons stated above with respect to the Executive
Officers. Mr. Cannon did not receive a discretionary bonus.

         Other Compensation Plans. The Company maintains insurance and
retirement agreements with certain of its Executive Officers and managers,
including Mr. Cannon and the Named Executive Officers, which provide for payment
of a death benefit (net of premiums paid and recovered by the Company) to a
designated beneficiary or for payment of a retirement benefit upon reaching age
62. Geneva also has a number of other broad-based employee benefit plans in
which Executive Officers participate on the same terms as other employees
meeting the eligibility requirements, subject to any legal limitations on
amounts that may be contributed to or benefits payable under the plans.

         Submitted by the Compensation Committee of the Board of Directors:

                                        R.J. Shopf
                                        K. Fred Skousen
                                        Alan C. Ashton



                                       8
<PAGE>   10

PERFORMANCE GRAPH

         The following graph shows a comparison of cumulative total shareholder
return on the Company's Class A Common Stock, calculated on a dividend
reinvested basis, from September 30, 1993 through September 30, 1998, compared
with the S&P 500 Index and the S&P Steel Index.




                                     [GRAPH]
















<TABLE>
<CAPTION>
                                     SEP-93            SEP-94            SEP-95            SEP-96            SEP-97          SEP-98
<S>                                  <C>               <C>               <C>               <C>               <C>             <C> 
Geneva Steel                          $100              $147              $ 64              $ 26              $ 30            $ 10
S&P(R)500                             $100              $104              $135              $162              $227            $248
S&P(R)Iron & Steel Index              $100              $129              $ 91              $ 90              $105            $ 76
</TABLE>



                                       9
<PAGE>   11

ITEM 12.   SECURITY OWNERSHIP OF CERTAIN BENEFICIAL OWNERS AND MANAGEMENT

         The following table sets forth information as of January 19, 1999 with
respect to the beneficial ownership of shares of the Class A Common Stock and
Class B Common Stock by each person known by the Company to be the beneficial
owner of more than 5 percent of either of such classes of Common Stock, by each
director or nominee, by each of the Named Executive Officers, and by all
directors and officers as a group. The number of Class A Shares listed below
does not include Class A Shares issuable upon conversion of Class B Shares.
Unless otherwise noted, each person named has sole voting and investment power
with respect to the shares indicated. The percentages set forth below have been
computed based on the number of outstanding securities, excluding treasury
shares held by the Company, and are based on 14,975,265 shares of Class A Common
Stock and 18,451,348 shares of Class B Common Stock.

<TABLE>
<CAPTION>
                                                                         BENEFICIAL OWNERSHIP
                                                                        AS OF JANUARY 19, 1999*
                                                                    -------------------------------
                                                                   NUMBER OF         PERCENTAGE OF CLASS
NAME AND ADDRESS OF BENEFICIAL OWNER                                SHARES              OUTSTANDING
------------------------------------                                ------              -----------
<S>                                                              <C>                 <C>
CLASS A COMMON STOCK:
Robert J. Grow ...................................                 120,600(1)                **
Dennis L. Wanlass ................................                  88,600(2)                **
Alan C. Ashton ...................................                  50,000                   **
Ken C. Johnsen ...................................                  82,400(2)                **
Joseph A. Cannon .................................                  77,256(3)                **
R. J. Shopf ......................................                  15,000                   **
K. Fred Skousen ..................................                   2,500                   **
Kevin S. Flannery ................................                      --                   **
Gregory T. Hradsky ...............................                      --                   **
All directors and officers as a group (12 persons)                 535,956(4)

CLASS B COMMON STOCK(5):
Joseph A. Cannon .................................               9,442,204(6)              51.2
Robert J. Grow ...................................               8,855,319                 48.0
All directors and officers as a group (2 persons)               18,297,523                 99.2
</TABLE>

----------

*        Beneficial ownership as a percentage of the class for each person
         holding options exercisable within 60 days has been calculated as
         though shares subject to such options were outstanding, but such shares
         have not been deemed outstanding for the purpose of calculating the
         percentage of the class owned by any other person.
**       Less than 1% of outstanding shares.
(1)      Includes 100,000 shares subject to presently exercisable options and
         15,500 shares owned by Mr. Grow's spouse which may be deemed to be
         beneficially owned by him. Mr. Grow disclaims beneficial ownership of
         the shares owned by his spouse.
(2)      Subject to presently exercisable options.
(3)      Includes 3,156 shares held by Riverwood Limited Partnership, of which
         Joseph A. Cannon is general partner, and 74,000 shares subject to
         presently exercisable options.
(4)      Includes 443,400 shares subject to presently exercisable options.
(5)      The Class B Common Stock is convertible into Class A Common Stock at a
         rate of ten shares of Class B Common Stock for one share of Class A
         Common Stock. If they were to convert their shares of Class B Common
         Stock into shares of Class A Common Stock, Mr. Cannon would
         beneficially own 1,021,476 shares of Class A Common Stock (including
         shares owned by Riverwood Limited Partnership), Mr. Grow would
         beneficially own 1,011,632 shares of Class A Common Stock (including
         shares owned by his spouse), and all directors and officers as a group
         would beneficially own 2,033,108 shares of Class A Common Stock
         (including all shares subject to presently exercisable options). In the
         event of such conversions, Mr. Cannon would own 6.1% of the outstanding
         Class A Common Stock, Mr. Grow would own 6.0% of the outstanding Class
         A Common Stock, and all directors and officers as a group would own
         12.1% of the outstanding Class A Common Stock.
(6)      Includes 828,013 shares held by Riverwood Limited Partnership, of which
         Joseph A. Cannon is general partner.


         Joseph A. Cannon and Robert J. Grow together beneficially own 99.2% of
the outstanding shares of Class B Common Stock and 54.8% of the total voting
power of the Company. They are therefore able to determine the outcome of
fundamental corporate transactions such as the election of directors, amendments
of the Company's articles of incorporation (except for certain amendments which
are, by mandatory provisions of law, subject to a class vote of shareholders)
and sale of all or substantially all of the Company's assets, and to prevent
certain mergers or consolidations involving the Company.



                                       10
<PAGE>   12

ITEM 13.   CERTAIN RELATIONSHIPS AND RELATED TRANSACTIONS

         On September 27, 1996, the Company entered into an agreement to loan up
to $500,000 to Joseph A. Cannon, its Chief Executive Officer. On September 27,
1996, October 4, 1996 and December 23, 1996, the Company loaned $250,000,
$210,000 and $40,000, respectively. On February 13, 1997, the Company authorized
an increase in the loan amount to $700,000 and advanced an additional $200,000.
The loans were evidenced by promissory notes bearing interest at the rate of
8.53% and payable at the earlier of September 27, 1997 or demand for repayment
by the Company. The loans were secured by interests in real and personal
property owned by the Chief Executive Officer and an affiliated entity. On
October 17, 1997, the Chief Executive Officer paid $240,000 on the loans and the
payment date of the loans was extended to April 30, 1998. On December 17, 1997,
the Chief Executive Officer paid an additional $400,000 on the loans. On
November 24, 1998, the remaining balance was paid by the Chief Executive
Officer.



                                       11
<PAGE>   13

                                   SIGNATURES

         Pursuant to the requirements of Section 13 or 15(d) of the Securities
Exchange Act of 1934, as amended, the Registrant has duly caused this Amendment
No. 1 to Annual Report to be signed on its behalf by the undersigned, thereunder
duly authorized.

                                        GENEVA STEEL COMPANY



                                        By:  \s\ DENNIS L. WANLASS
                                           Vice President, Treasurer and Chief
                                           Financial Officer




Dated:            March 10, 1999



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