<PAGE>   1

                       SECURITIES AND EXCHANGE COMMISSION
                             Washington, D.C. 20549

                                    FORM 10-Q

(Mark One)

  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

Commission file number 0-14190

                         DREYER'S GRAND ICE CREAM, INC.
             (Exact name of registrant as specified in its charter)

Delaware                                          No. 94-2967523
(State or other jurisdiction of                   (I.R.S. Employer
incorporation or organization)                    Identification No.)


                 5929 College Avenue, Oakland, California 94618
              (Address of principal executive offices) (Zip Code)

                                 (510) 652-8187
              (Registrant's telephone number, including area code)


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.


<TABLE>
<CAPTION>
                                                   Shares Outstanding
                                                       May 8, 1998
                                                       -----------
<S>                                                    <C>       
        Common stock, $1.00 par value                  27,151,680
</TABLE>



<PAGE>   2

                         DREYER'S GRAND ICE CREAM, INC.



PART I:  FINANCIAL INFORMATION



ITEM 1.  FINANCIAL STATEMENTS



                         DREYER'S GRAND ICE CREAM, INC.

                           CONSOLIDATED BALANCE SHEET



<TABLE>
<CAPTION>
                                                        March 28, 1998       December 27, 1997
                                                        --------------       -----------------
($ in thousands, except per share amounts)               (unaudited)
<S>                                                    <C>                  <C>     
Assets
Current Assets:
      Cash and cash equivalents                           $  4,038               $  3,626
      Trade accounts receivable, net of
         allowance for doubtful accounts of
         $761 in 1998 and $710 in 1997                      94,681                 82,011
      Other accounts receivable                             20,304                 16,527
      Inventories                                           54,415                 49,720
      Prepaid expenses and other                            13,814                 14,416
                                                          --------               --------
      Total current assets                                 187,252                166,300

Property, plant and equipment, net                         236,206                232,826
Goodwill and distribution rights, net                       89,419                 89,932
Other assets                                                13,596                 13,740
                                                          --------               --------
Total assets                                              $526,473               $502,798
                                                          ========               ========
</TABLE>



See accompanying Notes to Consolidated Financial Statements



                                       2

<PAGE>   3

                         DREYER'S GRAND ICE CREAM, INC.

                           CONSOLIDATED BALANCE SHEET



<TABLE>
<CAPTION>
                                                                           March 28, 1998       December 27, 1997
                                                                           --------------       -----------------
                                                                            (unaudited)
<S>                                                                        <C>                   <C>   
($ in thousands, except per share amounts)

Liabilities and Stockholders' Equity
Current Liabilities:
     Accounts payable and accrued liabilities                                 $ 76,296               $ 57,037
     Accrued payroll and employee benefits                                      20,938                 22,323
     Current portion of long-term debt                                           8,364                  8,364
                                                                              --------               --------
     Total current liabilities                                                 105,598                 87,724

Long-term debt, less current portion                                           178,731                165,913
Deferred income taxes                                                           38,905                 40,591
                                                                              --------               -------- 
Total liabilities                                                              323,234                294,228
                                                                              --------               --------

Commitments and contingencies

Redeemable convertible preferred stock, $1 par
     value - 1,008,000 shares authorized; 1,008,000
     shares issued and outstanding in 1998 and 1997                             99,337                 99,230
                                                                              --------               --------

Stockholders' Equity:
     Preferred stock, $1 par value -
          8,992,000 shares authorized; no shares
          issued or outstanding in 1998 and 1997
     Common stock, $1 par value - 60,000,000 shares authorized;
          27,102,000 shares and 27,020,000 shares issued and
          outstanding in 1998 and 1997, respectively                            27,102                 27,020
     Capital in excess of par                                                   44,020                 42,822
     Retained earnings                                                          32,780                 39,498
                                                                              --------               --------
Total stockholders' equity                                                     103,902                109,340
                                                                              --------               --------
Total liabilities and stockholders' equity                                    $526,473               $502,798
                                                                              ========               ========
</TABLE>



See accompanying Notes to Consolidated Financial Statements



                                       3

<PAGE>   4

                         DREYER'S GRAND ICE CREAM, INC.

                      CONSOLIDATED STATEMENT OF OPERATIONS
                                   (unaudited)


<TABLE>
<CAPTION>
                                                                Thirteen Weeks Ended
                                                      ----------------------------------------
($ in thousands, except per share amounts)            March 28, 1998            March 29, 1997
                                                      --------------            --------------
<S>                                                      <C>                      <C>      
Revenues:
     Net sales                                           $ 215,082                $ 200,438
     Other income                                              677                      404
                                                         ---------                ---------
                                                           215,759                  200,842
                                                         ---------                ---------
Costs and expenses:
     Cost of goods sold                                    178,968                  162,251
     Selling, general and administrative                    43,452                   36,184
     Interest, net of interest capitalized                   2,667                    2,489
                                                         ---------                ---------
                                                           225,087                  200,924
                                                         ---------                ---------
Loss before income taxes                                    (9,328)                     (82)
Income tax benefit                                          (3,703)                     (32)
                                                         ---------                ---------
Net loss                                                    (5,625)                     (50)
Accretion of preferred stock to
     redemption value                                         (106)                    (106)
Preferred stock dividends                                     (174)                  (1,144)
                                                         ---------                ---------
Net loss applicable to common stock                      $  (5,905)               $  (1,300)
                                                         =========                =========
Net loss per common share:
     Basic                                               $    (.22)               $    (.05)
                                                         =========                =========
     Diluted                                             $    (.22)               $    (.05)
                                                         =========                =========
Dividends per common share                               $     .03                $     .03
                                                         =========                =========
</TABLE>


See accompanying Notes to Consolidated Financial Statements



                                       4

<PAGE>   5

                         DREYER'S GRAND ICE CREAM, INC.

            CONSOLIDATED STATEMENT OF CHANGES IN STOCKHOLDERS' EQUITY
                                   (unaudited)




<TABLE>
<CAPTION>
                                                   Common Stock            
                                              -----------------------      Capital in      Retained
(In thousands)                                 Shares         Amount      Excess of Par    Earnings         Total
                                              --------       --------       --------       --------       --------
<S>                                           <C>           <C>            <C>            <C>            <C>     
Balance at December 28, 1996                    13,345       $ 13,345       $ 51,956       $ 38,762       $104,063
      Net loss                                                                                  (50)           (50)
      Accretion of preferred stock
           to redemption value                                                                 (106)          (106)
      Preferred stock dividends declared                                                     (1,144)        (1,144)
      Common stock dividends declared                                                          (803)          (803)
      Repurchases and retirements
            of common stock                         (4)            (4)          (110)                         (114)
      Employee stock plans                          60             60          1,631                         1,691
                                              --------       --------       --------       --------       --------
Balance at March 29, 1997                       13,401       $ 13,401       $ 53,477       $ 36,659       $103,537
                                              ========       ========       ========       ========       ========

Balance at December 27, 1997                    27,020       $ 27,020       $ 42,822       $ 39,498       $109,340
      Net loss                                                                               (5,625)        (5,625)
      Accretion of preferred stock
            to redemption value                                                                (106)          (106)
      Preferred stock dividends declared                                                       (174)          (174)
      Common stock dividends declared                                                          (813)          (813)
      Employee stock plans                          82             82          1,198                         1,280
                                              --------      --------       --------       --------       --------
Balance at March 28, 1998                       27,102       $ 27,102       $ 44,020       $ 32,780       $103,902
                                              ========       ========       ========       ========       ========
</TABLE>

See accompanying Notes to Consolidated Financial Statements





                                       5
<PAGE>   6
                         DREYER'S GRAND ICE CREAM, INC.

                      CONSOLIDATED STATEMENT OF CASH FLOWS
                                   (unaudited)


<TABLE>
<CAPTION>
                                                                                Thirteen Weeks Ended
                                                                               -----------------------
($ in thousands)                                                               March 28,      March 29,
                                                                                 1998           1997
                                                                               --------       --------
<S>                                                                            <C>            <C>      
Cash flows from operating activities:
     Net loss                                                                  $ (5,625)      $    (50)
     Adjustments to reconcile net loss to cash from operations:
          Depreciation and amortization                                           8,406          7,618
          Deferred income taxes                                                  (1,686)           (17)
          Changes in assets and liabilities, net of amounts acquired:
                Trade accounts receivable                                       (12,670)       (14,576)
                Other accounts receivable                                        (3,777)         1,011
                Inventories                                                      (4,695)        (6,419)
                Prepaid expenses and other                                          602          2,210
                Accounts payable and accrued liabilities                         19,252         20,740
                Accrued payroll and employee benefits                            (1,385)         1,518
                                                                               --------       --------
                                                                                 (1,578)        12,035
                                                                               --------       --------
Cash flows from investing activities:
     Acquisition of property, plant and equipment                               (10,884)        (6,059)
     Retirement of property, plant and equipment                                    135            310
     Increase in goodwill and distribution rights                                  (299)           (96)
     Increase in other assets                                                       (81)          (436)
                                                                               --------       --------
                                                                                (11,129)        (6,281)
                                                                               --------       --------
Cash flows from financing activities:
     Proceeds from long-term debt                                                17,600
     Reductions in long-term debt                                                (4,782)        (7,889)
     Issuance of common stock under employee stock plans                          1,280          1,691
     Repurchases of common stock                                                                  (114)
     Cash dividends paid                                                           (979)        (1,944)
                                                                               --------       --------
                                                                                 13,119         (8,256)
                                                                               --------       --------

Increase (decrease) in cash and cash equivalents                                    412         (2,502)

Cash and cash equivalents, beginning of period                                    3,626          4,134
                                                                               --------       --------

Cash and cash equivalents, end of period                                       $  4,038       $  1,632
                                                                               ========       ========

Supplemental Cash Flow Information-
Cash paid (refunded) during the period for:
                Interest (net of amounts capitalized)                          $  1,883       $  1,960
                Income taxes (net of refunds)                                        85         (2,832)
</TABLE>



See accompanying Notes to Consolidated Financial Statements




                                       6


<PAGE>   7

                         DREYER'S GRAND ICE CREAM, INC.

                   NOTES TO CONSOLIDATED FINANCIAL STATEMENTS


NOTE 1 - General:

     Dreyer's Grand Ice Cream, Inc. and its subsidiaries (the Company) is a
single segment industry company engaged in the business of manufacturing and
distributing premium ice cream and other frozen dessert products to grocery and
convenience stores, foodservice accounts and independent distributors in the
United States.

The consolidated financial statements for the thirteen week periods ended March
28, 1998 and March 29, 1997 have not been audited by independent public
accountants, but include all adjustments, such as normal recurring accruals,
which management considers necessary for a fair presentation of the consolidated
operating results for the periods. The statements have been prepared by the
Company pursuant to the rules and regulations of the Securities and Exchange
Commission. Accordingly, certain information and footnote disclosure normally
included in financial statements prepared in conformity with generally accepted
accounting principles have been condensed or omitted pursuant to such rules and
regulations. The operating results for interim periods are not necessarily
indicative of results to be expected for an entire year. The aforementioned
statements should be read in conjunction with the Consolidated Financial
Statements for the year ended December 27, 1997, appearing in the Company's 1997
Annual Report to Stockholders.


NOTE 2 - Inventories:

     Inventories are stated at the lower of cost (determined by the first-in,
first-out method) or market. Inventories at March 28, 1998 and December 27, 1997
consisted of the following (in thousands):


<TABLE>
<CAPTION>
                                         March 28,        December 27, 
                                          1998                1997
                                         ---------        ------------ 
                                        (unaudited)
<S>                                      <C>                <C>    
               Raw materials             $ 8,211            $ 7,411
               Finished goods             46,204             42,309
                                         -------            -------

                                         $54,415            $49,720
                                         =======            =======
</TABLE>


NOTE 3 - Net Loss Per Common Share:

     Net loss per common share is computed using the weighted average number of
shares of common stock outstanding during the period, which were 27,041,000
shares for the quarter ended March 28, 1998 and 26,736,000 shares for the
quarter ended March 29, 1997. The potentially dilutive effect of the Company's
redeemable convertible preferred stock and other common stock equivalents was
anti-dilutive for the thirteen week periods ended March 28, 1998 and March 29,
1997. Accordingly, diluted net loss per common share is the same as basic net
loss per common share.



                                       7
<PAGE>   8



NOTE 4 - Preoperating Costs:

     In April 1998, the Accounting Standards Executive Committee issued
Statement of Position 98-5, "Reporting on the Costs of Start-Up Activities" (SOP
98-5). SOP 98-5 requires that the cost of start-up activities, including
preoperating costs, should be expensed as incurred. This new accounting standard
is effective for financial statements for periods beginning after December 15,
1998. The Company currently capitalizes preoperating costs incurred during the
construction and start-up of new manufacturing and distribution facilities and
amortizes these costs over three years. Upon adoption of SOP 98-5, the Company
will expense unamortized preoperating costs in the first quarter of 1999 as a
cumulative change in accounting principle. The Company does not expect the
adoption of SOP 98-5 to have a material adverse effect on its financial
position.








                                       8
<PAGE>   9




ITEM 2.  MANAGEMENT'S DISCUSSION AND ANALYSIS OF CONSOLIDATED FINANCIAL
               CONDITION AND RESULTS OF OPERATIONS


   The following table sets forth for the periods indicated the percent which
the items in the Consolidated Statement of Operations bear to net sales and the
percentage change of such items compared to the indicated prior period:



<TABLE>
<CAPTION>
                                                     Percentage of Net Sales        
                                                   ----------------------------     Period-to-Period
                                                      Thirteen Weeks Ended         Increase (Decrease)
                                                   ----------------------------    -------------------
                                                   March 28,          March 29,    Thirteen Weeks 1998
                                                     1998              1997         Compared to 1997
                                                   --------           ---------    -------------------
<S>                                                 <C>               <C>          <C> 
Revenues:
   Net sales                                        100.3%               7.3%               7.3%
   Other income                                       0.3                0.2               67.6
                                                    -----              -----               

Total revenue                                       100.3              100.2                7.4
                                                    -----              -----               


Costs and expenses:
   Cost of goods sold                                83.2               80.9               10.3
   Selling, general and administrative               20.2               18.1               20.1
   Interest, net of interest capitalized              1.2                1.2                7.2
                                                    -----              -----

Total costs and expenses                            104.6              100.2               12.0
                                                    -----              -----  


Loss before income taxes                             (4.3)              (0.0)                NM

Income tax benefit                                   (1.7)              (0.0)                NM
                                                    -----              ----- 

Net loss                                             (2.6)               0.0                 NM
                                                    -----              ----- 

Accretion of preferred stock
   to redemption value                                0.1                0.1                0.0

Preferred stock dividends                             0.1                0.6              (84.8)
                                                    -----              ----- 

Net loss applicable to
   common stock                                      (2.8)%             (0.7)%            (354.2)
                                                    =====              ===== 
</TABLE>



                                       9


<PAGE>   10

FORWARD LOOKING STATEMENTS

The Company may from time to time make written or oral forward-looking
statements. Written forward-looking statements may appear in documents filed
with the Securities and Exchange Commission, in press releases, and in reports
to stockholders. The Private Securities Litigation Reform Act of 1995 contains a
"safe harbor" for forward-looking statements upon which the Company relies in
making such disclosures. In accordance with this "safe harbor" provision, we
have identified that forward-looking statements are contained in this
Management's Discussion and Analysis of Consolidated Financial Condition and
Results of Operations. The Company undertakes no obligation to publicly revise
these forward-looking statements to reflect subsequent events or circumstances.

Also, in connection with this "safe harbor" provision, the Company
identifies important factors that could cause the Company's actual results to
differ materially from those contained in any forward-looking statement made by
or on behalf of the Company. Any such statement is qualified by reference to the
cautionary statement set forth below and in the Company's other filings with the
Securities and Exchange Commission.

RESULTS OF OPERATIONS

Strategic Plan

The Company embarked on a strategic plan (the Strategic Plan) during the second
quarter of 1994 to accelerate the sales of its brand throughout the country. The
key elements of this plan are: 1) to build a high margin brand with a leading
market share through effective consumer marketing activities, 2) to expand the
Company's direct-store-delivery distribution network to national scale and
enhance this capability with sophisticated information and logistics systems and
3) to introduce innovative new products. The potential benefits of the Strategic
Plan are increased market share and future earnings above those levels that
would be attained in the absence of the Strategic Plan.

The Company continues to make significant progress against the key elements of
the Strategic Plan. This progress has yielded a leading market share in a
consolidating industry. The Company's direct-store-delivery system has now
reached national scope and includes emerging category management and demand
management capabilities. The Company has launched a wide range of new product
initiatives including the national roll-outs of Whole Fruit Sorbet, Starbucks(R)
Ice Cream and Dreyer's and Edy's Homemade Ice Cream. In light of these
successes, the Company believes that the benefits under the Strategic Plan will
be realized in future years. However, no assurance can be given that the
expectations relative to future market share and earnings benefits of the
strategy will be achieved. The realization of the benefits will depend upon,
among other things, consumer purchase responsiveness to the Company's new
products and increased marketing and promotion expenditures, competitors'
marketing and promotion responses, market conditions affecting the price of the
Company's products, commodity costs and efficiencies achieved in manufacturing
and distribution operations.

Thirteen Weeks ended March 28, 1998 Compared with Thirteen Weeks Ended March 29,
1997

Consolidated net sales for the first quarter of 1998 increased by $14,644,000,
or 7%, to $215,082,000 from $200,438,000 for the same period last year. Sales of
the Company's branded products were 9%, or $11,333,000, higher than the
comparable quarter in 1997 and accounted for 77% of the overall increase. The
increase in sales of the Company's branded products related primarily to higher
unit sales in all markets due in part to the continued higher promotion spending
under the Company's Strategic Plan. The products that led this increase were
Dreyer's and Edy's Homemade Ice Cream and Dreyer's and Edy's Grand Ice Cream,
more than offsetting declines in sales of the Company's better-for-you frozen
yogurt, sugar free and fat free products. Sales of branded products purchased
from other manufacturers (partner brands) increased 4% due to increases in sale
of Ben and Jerry's Homemade(R) Superpremium products, partially offset by
declines in Healthy Choice(R) Lowfat Ice Cream sales. Sales of partner brands
represented 36% of consolidated net sales compared with 37% in the same period
last year. Wholesale prices for the Company's branded products remained
relatively unchanged between these periods, before the effect of increased trade
promotion expense. The effect of price increases for partner brands was not
significant.

Cost of goods sold increased $16,717,000, or 10%, over the first quarter of
1997, while the overall gross margin decreased to 16.8% from 19.1%. The gross
margin decreased due to lower margins on company brands in 1998 caused by higher
dairy costs and a shift in the mix of products.




                                       10
<PAGE>   11


Selling, general and administrative expenses in the first quarter of 1998 were
$7,268,000 or 20%, higher than in the same period of 1997. This increase related
primarily to significantly higher trade promotion expenses in the first quarter
of 1998 compared with the same period in 1997. Selling, general and
administrative expenses increased to 20% of total sales in 1998 as compared to
18% of total sales in 1997.

Interest expense increased $178,000, or 7%, over the first quarter of 1997, due
primarily to additional interest expense due to higher average borrowings on the
Company's line of credit.

The income tax benefit increased due to a correspondingly higher pre-tax loss in
1998. The effective tax rate increased to 39.7% for the first quarter of 1998
from 39.3% for the first quarter of 1997.


LIQUIDITY AND CAPITAL RESOURCES

     Working capital at March 28, 1998 increased $3,078,000 from year-end 1997
due primarily to the seasonal increase in accounts payable and accrued
liabilities partially offset by an increase in trade accounts receivable. Cash
was provided primarily from borrowings on the Company's line of credit and was
used to fund a $10,884,000 increase in property, plant and equipment.

At March 28, 1998, the Company had $4,038,000 in cash and cash equivalents, and
an unused credit line of $45,000,000. The Company believes that its credit line,
along with its liquid resources, internally generated cash and financing
capacity, are adequate to meet anticipated operating and capital requirements.




                                       11

<PAGE>   12

                                   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.


                                 DREYER'S GRAND ICE CREAM, INC.






Dated:  May 12, 1998            By: /s/ Timothy F. Kahn
                                    ------------------------------------------
                                    Timothy F. Kahn
                                    Vice President - Finance and
                                    Administration and Chief Financial Officer





                                       12
<PAGE>   13

PART II:  OTHER INFORMATION

ITEM        6.    EXHIBITS AND REPORTS ON FORM 8-K


            a. No reports on Form 8-K were filed by the Company during the
quarter ended March 28, 1998.

            b.   Exhibits

Exhibit No.       Description

10.1              Amended and Restated Credit Agreement dated as of March 27,
                  1998 by and among Dreyer's Grand Ice Cream, Inc., Bank of
                  America National Trust and Savings Association, as one of the
                  Banks and as Agent, ABN AMRO Bank, N.V., as one of the Banks
                  and as Co-Agent, Credit Suisse First Boston and Union Bank of
                  California, N.A.

27                Financial Data Schedule.