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

                                    FORM 10-Q

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

         For the quarterly period ended March 28, 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  333-04841
                                ------------

                                 SIMMONS COMPANY
--------------------------------------------------------------------------------
             (Exact name of registrant as specified in its charter)

           DELAWARE                                     06-1007444
-------------------------------             ------------------------------------
(State or other jurisdiction of             (I.R.S. Employer Identification No.)
incorporation or organization)

One Concourse Parkway, Suite 600, Atlanta, Georgia          30328
--------------------------------------------------       ----------
(Address of principal executive offices)                 (Zip Code)

        Registrant's telephone number, including area code (770) 512-7700
                                                           --------------

         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. [x] Yes [ ] No

         The number of shares of the registrant's common stock outstanding as of
May 12, 1998 was 31,964,452.


<PAGE>   2



PART I - FINANCIAL INFORMATION

Item 1.  Financial Statements.


                        Simmons Company and Subsidiaries
                 Condensed Consolidated Statements of Operations
                                 (in thousands)
                                   (Unaudited)

<TABLE>
<CAPTION>

                                                            Quarter Ended
                                                     March 28,        March 29,
                                                        1998             1997
                                                     ---------        ---------

<S>                                                  <C>              <C>      
Net sales                                            $ 139,392        $ 133,416

Costs and expenses:
     Cost of products sold                              83,435           80,775
     Selling, general and administrative                51,068           47,555
     ESOP expense                                        1,475            1,251
     Amortization of intangible assets                   1,908            1,958
                                                     ---------        ---------
                                                       137,886          131,539
                                                     ---------        ---------
          Income from operations                         1,506            1,877

Interest expense, net                                    4,643            4,803
Other deductions, net                                      408              379
                                                     ---------        ---------

Loss before income taxes                                (3,545)          (3,305)

Provision for income taxes (benefit)                    (1,719)          (1,603)
                                                     ---------        ---------

Net loss                                             $  (1,826)       $  (1,702)
                                                     =========        =========
</TABLE>










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

                                        2

<PAGE>   3



                        Simmons Company and Subsidiaries
                      Condensed Consolidated Balance Sheets
                                 (in thousands)
                                   (Unaudited)

<TABLE>
<CAPTION>

                                                          March 28,   December 27,
                                                            1998          1997
                                                          --------      --------
<S>                                                       <C>           <C>     
ASSETS
Current assets:
     Cash and cash equivalents                            $  8,797      $  9,108
     Accounts receivable, less allowance for
        doubtful accounts of  $4,738 and $3,938             71,157        65,488
     Inventories                                            21,493        19,970
     Other current assets                                   19,312        17,037
                                                          --------      --------
         Total current assets                              120,759       111,603

Property, plant and equipment, net                          48,902        47,564
Patents, net of accumulated amortization of
      $5,570 and $4,870                                     11,462        12,162
Goodwill, net of accumulated amortization of
     $9,665 and $8,457                                     183,642       184,850
Deferred income taxes                                        6,051         8,453
Other assets                                                10,087        10,493
                                                          --------      --------
                                                          $380,903      $375,125
                                                          ========      ========
</TABLE>


















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

                                        3

<PAGE>   4



                        Simmons Company and Subsidiaries
                      Condensed Consolidated Balance Sheets
                                 (in thousands)
                                   (Unaudited)

<TABLE>
<CAPTION>

                                                                 March 28,    December 27,
                                                                    1998           1997
                                                                 ---------      ---------
<S>                                                              <C>            <C>      
LIABILITIES AND STOCKHOLDERS' EQUITY
Current liabilities:
     Accounts payable                                            $  20,535      $  27,847
     Accrued advertising and incentives                             21,349         15,457
     Accrued interest expense                                        6,166          3,793
     Other accrued expenses                                         20,093         18,265
     Current maturities of long-term obligations                     6,886         10,873
                                                                 ---------      ---------
         Total current liabilities                                  75,029         76,235

Noncurrent liabilities:
     Long-term obligations                                         182,753        173,570
     Other noncurrent liabilities                                   19,625         21,476
                                                                 ---------      ---------
         Total liabilities                                         277,407        271,281
                                                                 ---------      ---------

Series A Preferred Stock--ESOP, net of related
     unearned compensation of $15,647 and $17,122                   12,705         11,230

Common stockholders' equity:
     Common stock, $.01 par value; 50,000 shares authorized,
         31,964 shares issued                                          320            320
     Additional paid-in capital                                     84,680         84,680
     Retained earnings                                               5,848          7,674
     Accumulated other comprehensive income                            (51)           (55)
     Treasury stock                                                     (6)            (5)
                                                                 ---------      ---------
         Total common stockholders' equity                          90,791         92,614
                                                                 ---------      ---------
                                                                 $ 380,903      $ 375,125
                                                                 =========      =========
</TABLE>









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

                                        4

<PAGE>   5



                        Simmons Company and Subsidiaries
                 Condensed Consolidated Statements of Cash Flows
                                 (in thousands)
                                   (Unaudited)

<TABLE>
<CAPTION>

                                                            Quarter Ended
                                                        March 28,     March 29,
                                                          1998          1997
                                                        --------      --------

<S>                                                     <C>           <C>     
Net cash provided by (used in) operating activities     $ (1,755)     $ 11,336
                                                        --------      --------

Cash flows from investing activities:
     Purchases of property, plant and equipment           (3,755)       (2,489)
                                                        --------      --------
         Net cash (used in) investing activities          (3,755)       (2,489)
                                                        --------      --------

Cash flows from financing activities:
     Proceeds of long-term borrowings                      9,204         5,000
     Payments of long-term borrowings                     (4,008)       (9,021)
     Treasury stock purchases                                 (1)         --
                                                        --------      --------
         Net cash provided by (used in) financing
              activities                                   5,195        (4,021)
                                                        --------      --------

Net effect of exchange rate changes on cash                    4           (13)
                                                        --------      --------

Change in cash and cash equivalents                         (311)        4,813

Cash and cash equivalents, beginning of period             9,108         4,573
                                                        --------      --------
Cash and cash equivalents, end of period                $  8,797      $  9,386
                                                        ========      ========

Supplemental cash flow information:
     Depreciation                                       $  2,195      $  1,163
                                                        ========      ========
</TABLE>












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

                                        5

<PAGE>   6




                        Simmons Company and Subsidiaries
              Notes to Condensed Consolidated Financial Statements
                                   (Unaudited)

1.       Basis of Presentation

         For purposes of this report the "Company" refers to Simmons Company and
Subsidiaries, collectively.

         The Condensed Consolidated Financial Statements of the Company have
been prepared in accordance with the rules and regulations of the Securities and
Exchange Commission (the "SEC"). The accompanying unaudited condensed
consolidated financial statements contain all adjustments which, in the opinion
of management, are necessary to present fairly the financial position of the
Company at March 28, 1998, and its results of operations and cash flows for the
periods presented herein. All adjustments in the periods presented herein are
normal and recurring in nature unless otherwise disclosed. These condensed
consolidated financial statements should be read in conjunction with the
year-end consolidated financial statements and accompanying notes included in
the Company's annual report on Form 10-K, dated December 27, 1997. Operating
results for the period ended March 28, 1998, are not necessarily indicative of
future results that may be expected for the year ending December 26, 1998.

2.       Inventories

         Inventories consisted of the following at March 28, 1998 and December
         27, 1997 (in thousands):


<TABLE>
<CAPTION>
                                                          March 28,     December 27,
                                                            1998            1997
                                                         ---------       ---------
<S>                                                        <C>             <C>    
          Raw materials                                    $14,252         $12,209
          Work in progress                                   1,564           1,531
          Finished goods                                     5,677           6,230
                                                           -------         -------
                                                           $21,493         $19,970
                                                           =======         =======
</TABLE>
                                        
3.       Long-Term Obligations

         Long-term obligations consisted of the following at March 28, 1998 and
         December 27, 1997 (in thousands):

<TABLE>
<CAPTION>

                                                          March 28,    December 27,
                                                            1998            1997
                                                         ---------       ---------
<S>                                                      <C>             <C>      
          Senior loans:                                              
               Tranche A term loan                       $  31,057       $  33,000
               Tranche B term loan                          32,656          34,700
               Revolving loan                                8,000            --
          10.75% Series A Senior Subordinated                        
                Notes due 2006                             100,000         100,000
          Industrial Revenue Bonds, 7.00%, due 2017          9,700           9,700
          Industrial Revenue Bonds, 3.80%, due 2016          5,000           5,000
          Construction loan                                  2,533           1,329
          Other, including capital lease obligations           693             714
                                                         ---------       ---------
                                                           189,639         184,443
          Less current portion                              (6,886)        (10,873)
                                                         ---------       ---------
                                                         $ 182,753       $ 173,570
                                                         =========       =========
</TABLE>

                                        6

<PAGE>   7

                        Simmons Company and Subsidiaries
        Notes to Condensed Consolidated Financial Statements - Continued
                                   (Unaudited)


         The interest rates per annum in effect at March 28, 1998 for the
revolving credit, Tranche A term, and Tranche B term loans were 9.75%, 8.19%,
and 8.93%, respectively.

         At March 28, 1998, the amount under the revolving credit portion of the
Senior Credit Facility that was available to be drawn was approximately $28.1
million, after giving effect to $8.0 million of borrowings and $3.9 million that
was reserved for the Company's reimbursement obligations with respect to
outstanding letters of credit. The remaining availability under the revolving
credit facility may be utilized to meet the Company's current working capital
requirements, including issuance of stand-by and trade letters of credit. The
Company also may utilize the remaining availability under the revolving credit
facility to fund acquisitions and capital expenditures.

         The Senior Credit Facility contains certain covenants and restrictions
on actions by the Company and its subsidiaries. In addition, the Senior Credit
Facility requires that the Company comply with specified financial ratios and
tests, including minimum cash flow, a maximum ratio of indebtedness to cash flow
and a minimum interest coverage ratio. As of March 28, 1998, the Company was in
compliance with respect to all covenants under the Senior Credit Facility.

         In December 1997, Simmons Caribbean Bedding, Inc., a wholly owned
subsidiary of the Company, entered into a construction loan facility in the
amount of $3.2 million, which will be converted into a permanent loan upon
completion of a new facility and new equipment installation. As of March 28,
1998, approximately $2.5 million was drawn against the loan facility and is
accruing interest at a fluctuating rate equal to two hundred basis points (200)
over the London Interbank Offered Rate (or LIBOR), adjusted every ninety (90)
days.

Future maturities of long-term obligations as of March 28, 1998 are as follows
(in thousands):

<TABLE>
<S>               <C>                        <C>      
                  1998                       $  6,886
                  1999                          8,777
                  2000                         10,669
                  2001                         21,879
                  2002                         16,150
                  Thereafter                  125,278
                                             --------
                                             $189,639
                                             ========
</TABLE>

4.       Accounting Pronouncements

         In June 1997, the Financial Accounting Standards Board ("FASB") issued
Statement of Financial Accounting Standards ("SFAS") No. 130, "Reporting
Comprehensive Income." SFAS No. 130 establishes standards for reporting and
display of comprehensive income and its components in the financial statements.
SFAS No. 130 is effective for the Company's fiscal year beginning December 28,
1997. Reclassification of financial statements for earlier periods presented for
comparative purposes is required. The Company has adopted SFAS No. 130.

         In June 1997, the FASB issued SFAS No. 131, "Disclosure about Segments
of an Enterprise and Related Information." SFAS No. 131 establishes standards
for public business enterprises to report information about operating segments
in annual and interim financial statements. It also establishes standards for
related disclosures about products and services and geographic areas. SFAS No.
131 is required to be applied beginning with the Company's annual financial
statements for the

                                        7

<PAGE>   8



1998 fiscal year. Financial statement disclosures for prior periods are required
to be restated. The Company has evaluated the disclosure requirements and has
concluded that the Company operates in only one segment. The adoption of SFAS
No. 131 will have no material impact on the Company's consolidated results of
operations, financial position or cash flows.

         In February 1998, the FASB issued SFAS No. 132, "Employers' Disclosure
about Pensions and Other Post Retirement Benefits." SFAS No. 132 standardizes
the disclosure requirements for pensions and other post retirement benefits to
the extent practicable. This standard is effective beginning with the Company's
annual financial statements for the 1998 fiscal year, and prior period
disclosures are required to be restated. Management is currently reviewing the
provisions of SFAS No. 132 and does not believe that the adoption of SFAS No.
132 will have a material impact on the Company's financial statements.


                                        8

<PAGE>   9



Item 2. Management's Discussion and Analysis of Financial Condition and Results
        of Operations

QUARTER ENDED MARCH 28, 1998 AS COMPARED TO QUARTER ENDED MARCH 29, 1997

         Net Sales. Net sales for the quarter ended March 28, 1998 increased
4.5%, or $6.0 million, from $133.4 million in 1997 to $139.4 million in 1998.
This increase was due primarily to a 6.5% or $8.4 million increase in bedding
average unit selling price, offset, in part, by a 2.0% or $2.7 million decrease
in bedding unit sales volume. The growth in bedding average unit selling price
resulted primarily from new product introductions and a shift in mix of
Beautyrest(R) and BackCare(R) to higher end price points. The decrease in
bedding unit sales volume is predominantly attributable to an increased emphasis
on sales of higher end products.

         Cost of Goods Sold. As a percentage of net sales, cost of goods sold
for the quarter ended March 28, 1998 decreased 0.6 percentage point from 60.5%
in 1997 to 59.9% in 1998. The improvement in cost of goods sold as a percentage
of net sales is primarily attributable to the growth in bedding average unit
selling price resulting from a shift in mix of Beautyrest(R) and BackCare(R) to
higher end price points. Offsetting this improvement, in part, were temporary
inefficiencies as a result of plant relocations.

         Selling, General and Administrative Expenses. As a percentage of net
sales, selling, general and administrative expenses for the quarter ended March
28, 1998 increased 1.0 percentage point from 35.6% in 1997 to 36.6% in 1998. The
increase in selling, general and administrative expenses is attributable to an
increase in marketing expenditures and higher depreciation expense. The increase
in marketing expenditures is a result of higher cooperative advertising and
promotions. The increase in depreciation is the result of the commencement of
amortizing the systems upgrade project.

         ESOP Expense. ESOP expense for the quarter ended March 28, 1998
increased from approximately $1.3 million in 1997 to $1.5 million due primarily
to an increase in the number of eligible participants in the plan.

         Interest Expense, Net. Interest expense, net decreased approximately
$0.2 million to $4.6 million due primarily to lower short-term borrowings during
the quarter.

         Provision (Benefit) for Income Taxes. The Company's effective tax rates
for the quarters ended March 28, 1998 and March 29, 1997 differ from the federal
statutory rate primarily because of non tax-deductible amortization of goodwill.

         Net (Loss) Income. For the reasons set forth above, the quarter ended
March 28, 1998 resulted in a net loss of $1.8 million as compared to $1.7
million at March 29, 1997.

LIQUIDITY AND CAPITAL RESOURCES

         The Company's primary source of cash to fund its liquidity needs is net
cash provided by operating activities and availability under its revolving
credit facility. Net cash used in operating activities was $1.8 million for the
quarter ended March 28, 1998 compared to $11.3 million provided by operating
activities in 1997, due primarily to the timing of accounts receivable
collections and the timing of payments of accounts payable and accrued
liabilities. The Company's principal use of funds consists of payments of
principal, interest, and capital expenditures. Capital expenditures totaled $3.8
million for the quarter ended March 28, 1998. These capital expenditures
consisted primarily of normal recurring capital expenditures in the amount of
$1.6 million, capital expenditures relating to the construction of a new
manufacturing facility in the amount of $1.2 million and capitalized
expenditures related to the Company's systems upgrade project in the amount of
$1.0 million. The

                                        9

<PAGE>   10


                        Simmons Company and Subsidiaries
                     Management's Discussion and Analysis of
            Financial Condition and Results of Operations - Continued

Company estimates that total normal recurring capital expenditures will be
approximately $7.0 million in 1998. In addition, total expenditures for
completing the systems upgrade project are expected to be approximately $2.3
million in 1998. Management believes that annual capital expenditure limitations
in its Senior Credit Facility will not significantly inhibit the Company from
meeting its ongoing capital needs.

         The Company may seek to make selective acquisitions in the bedding
industry. Although the Company has discussions from time to time with potential
candidates, the Company currently has no commitments with respect to any such
acquisitions.

         At March 28, 1998, the amount under the revolving credit portion of the
Senior Credit Facility that was available to be drawn was approximately $28.1
million, after giving effect to $8.0 million of borrowings and $3.9 million that
was reserved for the Company's reimbursement obligations with respect to
outstanding letters of credit. The remaining availability under the revolving
credit facility may be utilized to meet the Company's current working capital
requirements, including issuance of stand-by and trade letters of credit. The
Company also may utilize the remaining availability under the revolving credit
facility to fund acquisitions and capital expenditures. At March 28, 1998, the
Company's weighted average borrowing cost was 9.6%.

         The Senior Credit Facility contains certain covenants and restrictions
on actions by the Company and its subsidiaries. In addition, the Senior Credit
Facility requires that the Company comply with specified financial ratios and
tests, including minimum cash flow, a maximum ratio of indebtedness to cash flow
and a minimum interest coverage ratio. On March 28, 1998, in compliance with a
covenant pertaining to excess cash flow contained in the Senior Credit Facility,
the Company made a prepayment of approximately $4.0 million on the term loans.
The payment was applied ratably to Tranche A and Tranche B term loans and on a
pro-rata basis reduced subsequent scheduled principal payments. As of March 28,
1998, the Company was in compliance with respect to all covenants under the
Senior Credit Facility.

         In December 1997, Simmons Caribbean Bedding, Inc., a wholly owned
subsidiary of the Company, entered into a construction loan facility in the
amount of $3.2 million, which will be converted into a permanent loan upon
completion of a new facility and new equipment installation. As of March 28,
1998, approximately $2.5 million was drawn against the loan facility and is
accruing interest at a fluctuating rate equal to two hundred basis points (200)
over the London Interbank Offered Rate (or LIBOR), adjusted every ninety (90)
days.

         Management believes that the Company will have the necessary liquidity
for the foreseeable future from cash flow from operations, and amounts available
under its revolving credit facility in the Senior Credit Facility to fund: (I)
its obligations under the Senior Credit Facility and the New Notes; (ii)
expected capital expenditures; (iii) selective acquisitions in the bedding
industry; and (iv) other needs required to manage and operate its business.

         Forward looking statements in this Form 10-Q are made pursuant to the
safe harbor provisions of the Private Securities Litigation Reform Act of 1995.
There are certain important factors that could cause results to differ from
those anticipated by some of the statements made above. Investors are cautioned
that all forward looking statements involve risk and uncertainty. In addition to
the factors discussed above, among the other factors that could cause actual
results to differ are the following: consumer spending and debt levels;
continuity of relationships with and purchases by major customers; product mix;
competitive pressure on sales and pricing, and increase in material or
production cost which cannot be recouped in product pricing.

                                       10

<PAGE>   11



PART II - OTHER INFORMATION

Item 1.       Legal Proceedings.

              None.

Item 5.       Other Information.

              None.

Item 6.       Exhibits and Reports on Form 8-K

              (a)     Exhibits:

                      27.0     Financial Data Schedule

              (b)     Reports on Form 8-K:

                      None.

                                       11

<PAGE>   12


                                   SIGNATURES

Pursuant to the requirements of Section 13 or 15(d) of the Securities Exchange
Act of 1934, Simmons Company has duly caused this report to be signed on its
behalf by the undersigned thereunto duly authorized.

                                 SIMMONS COMPANY



By:              /s/  Zenon S. Nie
         -------------------------------------
                       Zenon S. Nie
         Chairman of the Board of Directors,
         Chief Executive Officer and Director
               (Principal Executive Officer)



By:               /s/ Jonathan C. Daiker
         -------------------------------------
                   Jonathan C. Daiker
         Executive Vice President-Finance and
         Administration, Chief Financial Officer
                       and Director
               (Principal Accounting Officer)

Date:    May 12, 1998

                                       12