<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 31, 1998
                                       or
[ ] Transition Report Pursuant to Section 13 or 15(d) of the Securities
    Exchange Act of 1934

For the transition period from         to

Commission File Number               1-6417

                          GTE CALIFORNIA INCORPORATED
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

                CALIFORNIA                              95-0510200
  (STATE OR OTHER JURISDICTION OF       (I.R.S. EMPLOYER IDENTIFICATION NO.)
  INCORPORATION OR ORGANIZATION)

600 Hidden Ridge, HQE04B12 - Irving, Texas                75038
 (ADDRESS OF PRINCIPAL EXECUTIVE OFFICES)               (ZIP CODE)

Registrant's telephone number, including area code     972-718-5600


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





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 [ ]

The Company had 70,000,000 shares of $20 par value common stock outstanding at
April 30, 1998.  The Company's common stock is 100% owned by GTE Corporation.
<PAGE>   2
PART I.  FINANCIAL INFORMATION

GTE California Incorporated and Subsidiary
CONDENSED CONSOLIDATED STATEMENTS OF INCOME

<TABLE>
<CAPTION>
                                                           Three Months Ended
                                                               March 31,
                                                       -------------------------
                                                          1998           1997
                                                       ----------     ----------
                                                         (Thousands of Dollars)
<S>                                                    <C>            <C>       
REVENUES AND SALES
  Local services                                       $  354,286     $  359,625
  Network access services                                 211,621        221,589
  Toll services                                            77,613        117,313
  Other services and sales                                 91,748         82,555
                                                       ----------     ----------
   Total revenues and sales                               735,268        781,082
                                                       ----------     ----------


OPERATING COSTS AND EXPENSES
  Cost of services and sales                              278,458        251,166
  Selling, general and administrative                     105,421        123,879
  Depreciation and amortization                           143,607        165,073
                                                       ----------     ----------
   Total operating costs and expenses                     527,486        540,118
                                                       ----------     ----------
OPERATING INCOME                                          207,782        240,964

OTHER EXPENSE
  Interest - net                                           27,118         24,818
                                                       ----------     ----------
INCOME BEFORE INCOME TAXES                                180,664        216,146
  Income taxes                                             72,568         87,849
                                                       ----------     ----------
NET INCOME
                                                       $  108,096     $  128,297
                                                       ==========     ==========
</TABLE>





Per share data is omitted since the Company's common stock is 100% owned by GTE
Corporation (GTE).

See Notes to Condensed Consolidated Financial Statements.


                                        1
<PAGE>   3
GTE California Incorporated and Subsidiary

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS
(Dollars in Millions)

RESULTS OF OPERATIONS

<TABLE>
<CAPTION>
                                          Three Months Ended
                                              March 31,
                                       ------------------------
                                         1998           1997
                                       ----------     ---------
         <S>                           <C>            <C>
         Net income                    $    108.1     $   128.3
</TABLE>

Net income decreased 16% or $20.2 for the three months ended March 31, 1998,
compared to the same period in 1997. The three month decrease is primarily due
to lower toll revenues resulting from the effects of greater competition and
revenue reductions associated with regulatory mandates, partially offset by
customer growth in access lines and minutes of use and decreases in operating
costs and expenses.

REVENUES AND SALES

<TABLE>
<CAPTION>
                                                   Three Months Ended
                                                        March 31,
                                               ----------------------------
                                                  1998              1997
                                               ---------         ----------
<S>                                            <C>               <C>       
         Local services                        $   354.3         $    359.6
         Network access services                   211.6              221.6
         Toll services                              77.6              117.3
         Other services and sales                   91.8               82.6
                                               ---------         ----------

          Total revenues and sales             $   735.3         $    781.1
</TABLE>

Total revenues and sales decreased  6% or $45.8 for the three months ended
March 31, 1998, compared to the same period in 1997.

Local service revenues decreased 1% or $5.3 for the three months ended March
31, 1998, compared to the same period in 1997.  The decline is partially due to
$5.7 in reduced support payments from the California High Cost Fund for
providing universal service to customers in rural areas and a $4.9 decrease
relating to the termination in 1997 of Extended Area Service transitional
support payments.  Revenues from directory assistance and operator services
declined by $3 and revenues from non-recurring service charges decreased by
$3.6.  In addition, the impact of the California Public Utilities Commission's
(CPUC's) Implementation Rate Design supplement, recorded in the first quarter
of 1997, contributed $4.4 to the decrease.  These decreases were partially
offset by a 5.3% growth in access lines which generated additional revenues of
$5.9 from basic local services, $5.8 from CentraNet(R) services and $2.8 from
Integrated Services Digital Network (ISDN) and Digital Channel Services (DCS).
Revenues from SmartCall(R) and CLASS services, such as caller ID and automatic
call return/redial, also increased by $2.7.

Network access service revenues decreased 5% or $10 for the three months ended
March 31, 1998, compared to the same period in 1997.  Revenues decreased $8.6
as a result of interstate access rate reductions from the 1997 Federal
Communications Commission (FCC) price cap.  In 1997, the FCC also ordered
significant changes that altered the structure of access charges collected by
the Company.  These changes, effective January 1, 1998, reduced and
restructured the per minute charges paid by long distance carriers and
implemented new per line charges.  Additionally, the FCC created a structure
that resulted in different access charges for residential primary and



                                       2
<PAGE>   4
MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)

secondary lines and single line and multi-line business access lines.  In
aggregate, these changes resulted in an $8.2 decrease in network access service
revenues during the first quarter of 1998.  A decrease of $34 resulting from the
sharing provisions of the FCC's 1996 and 1997 price caps was partially offset by
reserves of $10.3 which were established in the first quarter of 1997.  The
results also reflect a $3 decline in revenues from end-user access charges and a
$4.7 decrease in revenues from intrastate sharing arrangements.  These decreases
were partially offset by a 16% increase in minutes of use which generated
additional revenues of $16.8.  Special access revenues, driven by growing demand
for increased bandwidth services by Internet Service Providers (ISPs) and other
high capacity users, increased by $11.7.  In addition, revenues from the
National Exchange Carrier Association (NECA) increased by $13.3.

Toll service revenues decreased 34% or $39.7 for the three months ended March
31, 1998, compared to the same period in 1997.  The decrease is primarily
caused by reduced toll volumes resulting from the effects of intraLATA (local
access transport area) toll competition, including 10XXX and 1+
presubscription.

Other services and sales revenues increased 11% or $9.2 for the three months
ended March 31, 1998, compared to the same period in 1997, primarily due to a
$5.2 increase associated with the FCC's order on payphone compensation and a 
$3.6 increase in revenues from billing and collection services.

OPERATING COSTS AND EXPENSES

<TABLE>
<CAPTION>
                                                        Three Months Ended
                                                            March 31,
                                                   ----------------------------
                                                      1998              1997
                                                   ----------        ----------
<S>                                                <C>               <C>       
         Total operating costs and expenses        $    527.5        $    540.1
</TABLE>

Total operating costs and expenses declined 2% or $12.6 for the three months
ended March 31, 1998, compared to the same period in 1997.  Depreciation expense
decreased $21.5 due to depreciation rate changes, reflecting higher net salvage
values related to certain telephone plant and equipment, that became effective
in the third quarter of 1997.  Other factors contributing to the overall
decrease include $11.9 of administrative productivity gains, a $3.1 decline in
access charges incurred to terminate customers' intraLATA toll calls outside the
Company's service territory and a $9.1 reduction in employee benefit-related
expenses. These decreases were partially offset by an $11.2 rise in maintenance
and repair costs associated with storm damage within the Company's service
territories and a $13 increase in costs related to implementation of the FCC's
local number portability requirements. The decrease in total operating costs and
expenses was also partially offset by a $9.5 increase in Info Page billings from
directory publications.

OTHER EXPENSES

<TABLE>
<CAPTION>
                                                Three Months Ended
                                                     March 31,
                                           ---------------------------
                                              1998              1997
                                           ----------       ----------
<S>                                        <C>              <C>       
         Interest - net                    $     27.1       $     24.8
         Income taxes                            72.6             87.8
</TABLE>

Interest - net increased 9% or $2.3 for the three months ended March 31, 1998,
compared to the same period in 1997, primarily due to higher average short-term
debt levels.



                                       3
<PAGE>   5
MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)

Income taxes decreased 17% or $15.2 for the three months ended March 31, 1998,
compared to the same period in 1997, primarily due to a corresponding decrease
in pre-tax income.

CAPITAL RESOURCES AND LIQUIDITY

Management believes the Company has adequate internal and external resources
available to meet ongoing operating requirements for construction of new plant,
modernization of facilities and payment of dividends.  The Company generally
funds its construction program from operations, although external financing is
available. Short-term financings can be obtained through borrowings from the
Company's parent, GTE, or GTE Funding Incorporated, an affiliate of the
Company.  The Company participates with other affiliates in a $1,500, 364-day
syndicated line of credit.  In December 1997, the Company began participating
with GTE and other of its affiliates in a series of five bilateral credit
agreements for an additional $2,000 in credit capacity.  These facilities,
which are shared by the participating companies, are aligned with the maturity
date of the existing 364-day line of credit. The Company also has an existing
shelf registration statement for an additional $400 of debentures.

The Company's primary source of funds during the first three months of 1998 was
cash from operations of $257.2 compared to $336 for the same period in 1997.
This decrease in cash from operations reflects an increase in working capital
requirements combined with a decline in results from operations.

Net cash used in investing activities was $149 for the first three months of
1998, compared to $84.1 for the same period in 1997.  The increase in capital
expenditures reflects the Company's continued growth in primary and secondary
access lines and the modernization of interoffice facilities to mitigate
Internet congestion.  Although the capital expenditures during the first three
months of 1998 were higher than the same period in 1997, the overall
anticipated capital expenditures for 1998 are expected to be comparable to
the total capital expenditures incurred during 1997.

Net cash used in financing activities was $112.4 for the three months ended
March 31, 1998, compared to $184.1 during the same period in 1997. This included
dividend payments of $158.4 for the first three months of 1998, compared to
$112.9 for the same period in 1997.  Short-term financings, including the net
change in affiliate notes, increased $195.9 in the first quarter of 1998,
compared to a decrease of $71.1 for the same period in 1997. The Company also
retired $150 of long-term debt during the first quarter of 1998.

In its April 2, 1998 filing on Form 8-K, the Company's parent, GTE, stated that
because the MCI shareholders had accepted a competing offer, GTE's offer for
MCI was no longer outstanding.  As a result, the Company and GTE were removed
from "Credit Watch" by all rating agencies.  The Company believes that its
present investment grade credit rating provides ready access to the capital
markets at reasonable rates and provides the Company with the financial
flexibility necessary to pursue growth opportunities as they arise.

OTHER MATTERS

New Regulatory Framework (NRF)

Effective January 1, 1990, the CPUC adopted the NRF for the Company. Under the
NRF, rates are adjusted annually by the Price Cap Index (PCI), which is based
on inflation minus a productivity improvement factor.  Rates for partially
competitive services, such as Centrex and custom calling features, may be
priced below the price cap within a range set by the CPUC.  Rates are also
adjusted for exogenous events that are beyond the control of management as
defined in this plan.  Fully competitive services, such as directory
advertising, are not subject to pricing limits set by the CPUC.





                                       4
<PAGE>   6
MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)

In March 1998, the CPUC opened an order initiating its triennial review of the
NRF.  The Company expects to file comments regarding the first phase of the NRF
review in May 1998.

Competition

In January 1998, the CPUC approved the Company's petition to operate both as a
reseller and facilities-based competitive local-exchange carrier (CLC) offering
local-exchange service within the territories of mid-sized local-exchange
carriers.  Authority to commence facilities-based service was effective
February 1, 1998 and authority to resell services was effective April 1, 1998,
upon the filing of tariffs.

Open Access and Network Architecture Development (OANAD) Proceeding

On September 15, 1997, the Company submitted cost studies for unbundled network
elements (UNEs) and retail services to the CPUC.  A final order on the Company's
UNE costs is anticipated in September 1998 and a final order on UNE prices is
anticipated in the first quarter of 1999.

In a separate phase of the OANAD proceeding, the CPUC allowed comments on
parties' Operational Support Systems (OSS) and Non-Recurring Cost (NRC) studies
which were submitted in September 1997.  The Company filed a pricing proposal
for OSS and NRCs in April 1998 along with testimony regarding what constitutes
a "reasonable markup" for UNEs, arbitrage and price floor determinations.  A
final order on these matters is expected in late 1998.

Other Developments

In March and April 1998, the Company took action to correct errors discovered in
certain specialty directories known as "Street Address" directories.  Less than
two percent of the Company's customers with non-published, non-listed and
non-address directory listings had their information accidentally printed in the
Street Address books, which are specialty marketing directories generally used
by a limited number of California businesses on a leased basis.  Once the full
scope of the errors was known, the Company took immediate action to develop and
implement a comprehensive plan to retrieve and replace the directories in
question.  This included seeking and obtaining a temporary restraining order
preventing the use, copying or distribution of these directories by any
remaining holders of these directories.  Efforts were also made to contact all
customers who had requested non-published, non-listed or non-address listings,
in addition to the small percentage impacted by the errors.  The financial
impact, if any, of potential CPUC or legal actions that may arise as a result of
this occurrence cannot be determined at this time.

RECENT DEVELOPMENTS

In April 1998, the Company's parent, GTE, announced a series of actions
designed to further sharpen its strategic focus and improve its competitive
position by repositioning non-strategic properties and reducing costs.  GTE
expects to generate after-tax proceeds of $2,000-$3,000 by selling
non-strategic or under-performing operations, and plans to reduce annual costs
by more than $500 through improved efficiencies and productivity while it
continues to invest in new high-growth opportunities.  The impact of this
announcement on the Company is unknown at this time.  GTE's management is
currently assessing its options and, as decisions are finalized regarding the
sale of non-strategic operations and cost reductions, the Company could be
affected.





                                       5
<PAGE>   7
GTE California Incorporated and Subsidiary
CONDENSED CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                                   March 31,       December 31,
                                                                     1998              1997
                                                                 ------------      ------------
                                                                      (Thousands of Dollars)
<S>                                                              <C>               <C>         
ASSETS
Current assets:
  Cash and temporary investments                                 $      5,657      $      9,871
  Receivables, less allowances of $56,921 and $65,169                 692,863           699,038
  Inventories and supplies                                             53,119            51,050
  Prepaid insurance                                                    40,289             6,529
  Prepaid taxes and other                                              11,827            28,870
                                                                 ------------      ------------
   Total current assets                                               803,755           795,358
                                                                 ------------      ------------

Property, plant and equipment, at cost                             10,203,275        10,077,872
   Accumulated depreciation                                        (6,395,438)       (6,278,551)
                                                                 ------------      ------------
   Total property, plant and equipment, net                         3,807,837         3,799,321
                                                                 ------------      ------------

Prepaid pension costs                                                 738,137           706,556
Other assets                                                           24,734            19,095
                                                                 ------------      ------------
Total assets                                                     $  5,374,463      $  5,320,330
                                                                 ============      ============

LIABILITIES AND SHAREHOLDERS' EQUITY
Current liabilities:
  Short-term obligations, including current maturities           $    277,861      $    246,052
  Accounts payable                                                    369,783           356,322
  Taxes payable                                                        78,503            26,760
  Accrued interest                                                     20,734            30,163
  Accrued payroll costs                                                93,004            89,221
  Dividends payable                                                   190,624           158,246
  Other                                                               251,851           258,122
                                                                 ------------      ------------
   Total current liabilities                                        1,282,360         1,164,886
                                                                 ------------      ------------

  Long-term debt                                                    1,466,786         1,466,679
  Deferred income taxes                                               420,612           394,883
  Employee benefit plans                                              230,753           225,425
  Other liabilities                                                   260,801           272,648
                                                                 ------------      ------------
   Total liabilities                                                3,661,312         3,524,521
                                                                 ------------      ------------

  Preferred stock                                                      49,984            49,984
  Common stock (70,000,000 shares issued)                           1,400,000         1,400,000
  Additional paid-in capital                                           82,239            82,239
  Retained earnings                                                   180,928           263,586
                                                                 ------------      ------------
   Total shareholders' equity                                       1,713,151         1,795,809
                                                                 ------------      ------------
Total liabilities and shareholders' equity                       $  5,374,463      $  5,320,330
                                                                 ============      ============
</TABLE>


See Notes to Condensed Consolidated Financial Statements.



                                        6
<PAGE>   8
GTE California Incorporated and Subsidiary
CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS

<TABLE>
<CAPTION>
                                                            Three Months Ended
                                                                 March 31,
                                                         ------------------------
                                                            1998           1997
                                                         ---------      ---------
                                                          (Thousands of Dollars)
<S>                                                      <C>            <C>      
OPERATIONS
  Net income                                             $ 108,096      $ 128,297
  Adjustments to reconcile net income
  to net cash from operations:
   Depreciation and amortization                           143,607        165,073
   Deferred income taxes                                    25,165         20,222
   Provision for uncollectible accounts                     15,616         19,044
   Changes in current assets and current liabilities       (38,868)        36,601
   Other - net                                               3,577        (33,233)
                                                         ---------      ---------
   Net cash from operations                                257,193        336,004
                                                         ---------      ---------

INVESTING
  Capital expenditures                                    (148,978)       (87,933)
  Proceeds from sale of assets                                --            3,794
                                                         ---------      ---------
   Net cash used in investing                             (148,978)       (84,139)
                                                         ---------      ---------

FINANCING
  Long-term debt retired                                  (149,990)           (71)
  Dividends                                               (158,376)      (112,886)
  Increase (decrease) in short-term obligations,
     excluding current maturities                          195,937        (71,111)
                                                         ---------      ---------
   Net cash used in financing                             (112,429)      (184,068)
                                                         ---------      ---------
Increase (decrease) in cash and cash equivalents            (4,214)        67,797

Cash and cash equivalents:
  Beginning of period                                        9,871         22,158
                                                         ---------      ---------
  End of period                                          $   5,657      $  89,955
                                                         =========      =========
</TABLE>





See Notes to Condensed Consolidated Financial Statements.



                                        7
<PAGE>   9
GTE California Incorporated and Subsidiary
NOTES TO CONDENSED CONSOLIDATED FINANCIAL STATEMENTS

(1)      BASIS OF PRESENTATION:

         The unaudited condensed consolidated financial statements included
         herein have been prepared by the Company pursuant to the rules and
         regulations of the Securities and Exchange Commission.  Certain
         information and footnote disclosures normally included in financial
         statements prepared in accordance with generally accepted accounting
         principles have been condensed or omitted pursuant to such rules and
         regulations.  However, in the opinion of management of the Company,
         the condensed consolidated financial statements include all
         adjustments, which consist only of normal recurring accruals,
         necessary to present fairly the financial information for such
         periods.  These condensed consolidated financial statements should be
         read in conjunction with the financial statements and the notes
         thereto included in the Company's 1997 Annual Report on Form 10-K.

         Reclassifications of prior year data have been made, where
         appropriate, to conform to the 1998 presentation.

(2)      DEBT:

         Long-term debt as of March 31, 1998 includes $200 million of
         short-term borrowings in the form of affiliate notes payable which the
         Company anticipates refinancing during the second quarter of 1998.
         These affiliate notes payable represent notes payable to GTE Funding
         Incorporated, a company that provides short-term financing and
         investment vehicles and cash management services for the Company and
         six of its affiliates.

(3)      RECENT ACCOUNTING PRONOUNCEMENT:

         In March 1998, the American Institute of Certified Public Accountants
         issued Statement of Position 98-1, "Accounting for the Costs of
         Computer Software Developed or Obtained for Internal Use" (SOP 98-1).
         SOP 98-1 defines internal-use software and establishes accounting
         standards for the costs of such software. The Company is currently
         assessing the impact of adopting SOP 98-1.




                                       8
<PAGE>   10



GTE California Incorporated and Subsidiary
PART II.  OTHER INFORMATION

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

   (a)    Exhibits required by Item 601 of Regulation S-K.

          12   Statement re: Calculation of the Consolidated Ratio of Earnings
               to Fixed Charges

          27   Financial Data Schedule

   (b)    The Company filed no reports on Form 8-K during the first quarter of
          1998.




                                       9
<PAGE>   11

                                    SIGNATURE


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.



                                                GTE California Incorporated
                                              ------------------------------
                                                       (Registrant)



Date:    May 11, 1998                                Stephen L. Shore
      ------------------                      ------------------------------
                                                     Stephen L. Shore
                                                        Controller
                                              (Principal Accounting Officer)




                                       10

<PAGE>   12

                               INDEX TO EXHIBITS

<TABLE>
<CAPTION>
EXHIBIT
NUMBER              DESCRIPTION
-------             -----------
<S>       <C>
  12      Statement re: Calculation of the Consolidated Ratio of Earnings to
          Fixed Charges

  27      Financial Data Schedule
</TABLE>