<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                     2-33059

                   GTE HAWAIIAN TELEPHONE COMPANY INCORPORATED
             (EXACT NAME OF REGISTRANT AS SPECIFIED IN ITS CHARTER)

                HAWAII                                  99-0049500
     (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)


The registrant, a wholly-owned subsidiary of GTE Corporation, meets the
conditions set forth in General Instruction H(1) (a) and (b) of Form 10-Q and is
therefore filing this form with reduced disclosure format pursuant to General
Instruction H(2).

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 10,000,000 shares of $25 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 Hawaiian Telephone Company Incorporated and Subsidiaries
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                            $  68,402       $  64,743
   Network access services                      49,047          40,512
   Toll services                                15,730          19,700
   Other services and sales                     27,136          24,991
                                             ---------       ---------
     Total revenues and sales                  160,315         149,946
                                             ---------       ---------

OPERATING COSTS AND EXPENSES
   Cost of services and sales                   70,821          61,484
   Selling, general and administrative          28,601          30,594
   Depreciation and amortization                29,111          30,361
                                             ---------       ---------
     Total operating costs and expenses        128,533         122,439
                                             ---------       ---------

OPERATING INCOME                                31,782          27,507

OTHER (INCOME) EXPENSE
   Interest - net                                9,613           9,303
   Other - net                                    (909)           (336)
                                             ---------       ---------
INCOME BEFORE INCOME TAXES                      23,078          18,540
   Income taxes                                  7,857           6,878
                                             ---------       ---------
NET INCOME                                   $  15,221       $  11,662
                                             =========       =========
</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 Hawaiian Telephone Company Incorporated and Subsidiaries

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                 $       15.2       $         11.7
</TABLE>

Net income increased 30% or $3.5 for the three months ended March 31, 1998,
compared to same period in 1997. The increase is primarily the result of higher
network access service revenues, partially offset by increased operating costs
and expenses.

REVENUES AND SALES

<TABLE>
<CAPTION>
                                               Three Months Ended
                                                    March 31,
                                       ---------------------------------      
                                            1998                1997
                                       --------------     --------------  
<S>                                    <C>                <C>           
         Local services                $         68.4     $         64.7
         Network access services                 49.1               40.5
         Toll services                           15.7               19.7
         Other services and sales                27.1               25.0
                                       ---------------    ---------------

           Total revenues and sales    $        160.3     $        149.9
</TABLE>

Total revenues and sales increased 7% or $10.4 for the three months ended March
31, 1998, compared to the same period in 1997.

Local service revenues increased 6% or $3.7 for the three months ended March 31,
1998, compared to the same period in 1997. This increase reflects a $1.5 growth
in revenues from custom calling features, such as SmartCall(R) services and a 3%
increase in access lines, which generated $1.2 in additional revenues.

Network access service revenues increased 21% or $8.6 for the three months ended
March 31, 1998, compared to the same period in 1997. Minutes of use increased 5%
generating $0.8 of additional revenue. Special access revenues grew $1.4 due to
greater demand for increased bandwidth by Internet Service Providers (ISPs) and
other high-capacity users. Increased access rates for dedicated private lines
contributed an additional $7 to the increase. Offsetting these increases was a
decrease of $2.5 resulting from the impact of interstate access rate reductions
from the 1997 Federal Communications Commission (FCC) price cap.

Toll service revenues decreased 20% or $4 for the three months ended March 31,
1998, compared to the same period in 1997, primarily due to a decline in
domestic toll volumes, resulting from continued competition with long distance
carriers authorized to provide interisland toll service on a 10XXX and 1+
presubscription basis. Additionally, the impacts of interisland toll price
reductions which were effective May 7, 1997 contributed to the decline in toll
service revenues.



                                       2
<PAGE>   4


GTE Hawaiian Telephone Company Incorporated and Subsidiaries

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)


Other services and sales revenues increased 8% or $2.1 for the three months
ended March 31, 1998, compared to the same period in 1997. The increase is
primarily attributable to a $1 increase related to the FCC's order on payphone
compensation and a $0.2 increase in billing and collection services.

OPERATING COSTS AND EXPENSES

<TABLE>
<CAPTION>
                                                                       Three Months Ended
                                                                            March 31,
                                                                ----------------------------------
                                                                     1998               1997
                                                                ---------------    ---------------
<S>                                                             <C>                <C>           
         Cost of services and sales                             $         70.8     $         61.5
         Selling, general and administrative                              28.6               30.6
         Depreciation and amortization                                    29.1               30.3
                                                                --------------     --------------

            Total operating costs and expenses                   $       128.5     $        122.4
</TABLE>


Total operating costs and expenses increased 5% or $6.1 for the three months
ended March 31, 1998, compared to the same period in 1997. The increase is
primarily due to $3.4 in costs related to the implementation of the FCC's local
number portability requirements and a $2.8 increase in operating taxes. A $2.1
increase in advertising costs aimed at stimulating sales of enhanced services
and preserving market share in an increasingly competitive environment also
contributed to the change. These increases were partially offset by a $1.9
decrease in depreciation expense, primarily due to a change in the estimated net
salvage values related to certain telephone plant and equipment which became
effective in the third quarter of 1997.

INCOME TAXES

<TABLE>
<CAPTION>
                                          Three Months Ended
                                               March 31,
                                   ----------------------------------
                                        1998               1997
                                   ---------------    ---------------
<S>                                <C>                <C>           
         Income taxes              $        7.9       $          6.9
</TABLE>


Income taxes increased 14% or $1 for the three months ended March 31, 1998,
compared to the same period in 1997. This increase is primarily due to a
corresponding increase in pre-tax income partially offset by other tax
adjustments.

OTHER MATTERS

Communications Infrastructure

In April 1998, the Public Utilities Commission (PUC) of the state of Hawaii
adopted an AT&T model as the state's cost study for calculating federal
universal service high cost support. The PUC ordered AT&T to modify this model
to comply with the FCC guidelines. The Company filed a motion with the PUC on
April 9, 1998 requesting that the Company be allowed to provide the input values
to any model submitted to the FCC for calculating federal universal service
support and requesting an opportunity to review and comment on AT&T's model
which had been previously submitted. The PUC's ruling on the Company's motion is
pending.


                                       3
<PAGE>   5


GTE Hawaiian Telephone Company Incorporated and Subsidiaries

MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION
AND RESULTS OF OPERATIONS (CONTINUED)


Arbitration Activity

In November 1997, Western Wireless Corporation (WWC) filed a motion to compel
the Company to implement arbitrated interconnection rates, to provide sanctions
of $6.8 for failure to comply with the orders issued by the PUC in its
arbitration docket, and to suspend the Standard Billing Agreement. On January
23, 1998, the PUC denied WWC's motion. On March 13, 1998, the PUC denied WWC's
motion for reconsideration of the January 1998 decision.

Rural Service Plans

Briefs were filed on April 14, 1998 related to the petitions filed by rural area
communities to determine the adequacy of the telecommunications services
provided by the Company in the South Kona and Puna districts of the island of
Hawaii.

Interstate and International Services

On July 1, 1997, the Commonwealth of the Northern Mariana Islands (CNMI) served
by Micronesia Telephone Company (MTC), a subsidiary of the Company, was
incorporated into the North American Numbering Plan under the 670 area code.
This area code was CNMI's former country code. With this change, MTC's customers
for the first time are able to dial anywhere within the United States on a 1+
basis instead of the 011+ international access. In addition, customers were able
to dial on a toll-free basis 800 numbers nationwide. On August 1, 1997, the CNMI
was rate integrated into the U.S. domestic rate structure.

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.

In its April 2, 1998 filing on Form 8-K, GTE, the Company's parent, 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.




                                       4

<PAGE>   6


GTE Hawaiian Telephone Company Incorporated and Subsidiaries
CONDENSED CONSOLIDATED BALANCE SHEETS

<TABLE>
<CAPTION>
                                                             March 31,       December 31,
                                                               1998              1997
                                                            -----------       -----------
                                                                (Thousands of Dollars)
<S>                                                         <C>               <C>        
ASSETS
Current assets:
  Cash and cash equivalents                                 $     3,152       $       672
  Receivables, less allowances of $5,340 and $8,596             181,573           215,928
  Inventories and supplies                                       14,956            15,030
  Prepaid  taxes                                                 16,850            16,264
  Other                                                          11,028             3,775
                                                            -----------       -----------
     Total current assets                                       227,559           251,669
                                                            -----------       -----------
Property, plant and equipment, at cost                        2,035,091         2,019,252
  Accumulated depreciation                                   (1,185,546)       (1,173,900)
                                                            -----------       -----------
     Total property, plant and equipment, net                   849,545           845,352
                                                            -----------       -----------
Prepaid pension costs                                           209,187           202,473
Other assets                                                      8,153             6,619
                                                            -----------       -----------
Total assets                                                $ 1,294,444       $ 1,306,113
                                                            ===========       ===========

LIABILITIES AND SHAREHOLDER'S EQUITY
Current liabilities:
  Short-term obligations, including current maturities      $    60,284       $    99,702
  Accounts payable                                               60,056            57,221
  Taxes payable                                                   3,272             1,818
  Accrued interest                                                4,054            10,375
  Accrued payroll costs                                          26,870            26,434
  Accrued dividends                                               5,641            10,803
  Other                                                          40,774            35,251
                                                            -----------       -----------

    Total current liabilities                                   200,951           241,604
                                                            -----------       -----------

  Long-term debt                                                509,523           510,184
  Deferred income taxes                                         151,178           130,065
  Other liabilities, primarily employee benefit plans            57,448            58,496
                                                            -----------       -----------


    Total liabilities                                           919,100           940,349
                                                            -----------       -----------

Shareholder's equity:
  Common stock (10,000,000 shares issued)                       250,000           250,000
  Additional paid-in capital                                     91,146            91,146
  Retained earnings                                              34,198            24,618
                                                            -----------       -----------

    Total shareholder's equity                                  375,344           365,764
                                                            -----------       -----------

Total liabilities and shareholder's equity                  $ 1,294,444       $ 1,306,113
                                                            ===========       ===========
</TABLE>




See Notes to Condensed Consolidated Financial Statements.


                                       5
<PAGE>   7


GTE Hawaiian Telephone Company Incorporated and Subsidiaries
CONDENSED CONSOLIDATED STATEMENTS OF CASH FLOWS

<TABLE>
<CAPTION>
                                                             Three Months Ended
                                                                  March 31,
                                                          ------------------------  
                                                             1998           1997
                                                          ---------      ---------
                                                           (Thousands of Dollars)
<S>                                                        <C>            <C>     
OPERATIONS
  Net income                                               $ 15,221       $ 11,662
  Adjustments to reconcile net income
  to net cash from operations:
    Depreciation and amortization                            29,111         30,361
    Deferred income taxes                                    20,747          2,593
    Provision for uncollectible accounts                      2,374          2,723
    Changes in current assets and current liabilities           859        (55,243)
    Other - net                                              (2,194)        (1,358)
                                                           --------       --------

    Net cash from (used in) operations                       66,118         (9,262)
                                                           --------       --------

INVESTING
  Capital expenditures                                      (37,323)       (29,365)
                                                           --------       --------

    Cash used in investing                                  (37,323)       (29,365)
                                                           --------       --------

FINANCING
  Long-term debt retired                                       (516)          (743)
  Increase (decrease) in short-term obligations,
    excluding current maturities                            (14,996)        28,349
  Dividends                                                 (10,803)        (5,327)
                                                           --------       --------

    Net cash from (used in) financing                       (26,315)        22,279
                                                           --------       --------

Increase (decrease) in cash and cash equivalents              2,480        (16,348)

Cash and cash equivalents:
  Beginning of period                                           672         20,154
                                                           --------       --------

  End of period                                            $  3,152       $  3,806
                                                           ========       ========
</TABLE>





See Notes to Condensed Consolidated Financial Statements.


                                       6
<PAGE>   8


GTE Hawaiian Telephone Company Incorporated and Subsidiaries
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 $40 million of short-term
         borrowings in the form of affiliate notes payable which the Company
         anticipates refinancing during 1998. These affiliate notes payable
         represent notes payable to the Company's parent, GTE.

(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.




                                       7

<PAGE>   9


GTE Hawaiian Telephone Company Incorporated and Subsidiaries
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.







                                       8


<PAGE>   10


                                    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 Hawaiian Telephone Company Incorporated
                                   --------------------------------------------
                                                 (Registrant)

Date:      May 15, 1998                     /s/ Stephen L. Shore
     --------------------          --------------------------------------------
                                                Stephen L. Shore
                                                   Controller
                                          (Principal Accounting Officer)






                                       9

<PAGE>   11





 EXHIBIT INDEX

    Exhibit
    Number                                  Description
----------------        --------------------------------------------------------

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

        27              Financial Data Schedule