<PAGE>   1
                                   FORM 10-Q
                       SECURITIES AND EXCHANGE COMMISSION
                            Washington, D.C.  20549

(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 31, 1998

     OR

/ /  TRANSITION REPORT PURSUANT TO SECTION 13 OR 15(d) OF THE SECURITIES
     EXCHANGE ACT OF 1934



Commission File Number                      1-13071

                         HANOVER COMPRESSOR COMPANY
           (Exact name of registrant as specified in its charter)


                     Delaware                                 75-2344249
       (State or other jurisdiction of                  (I.R.S. Employer
       incorporation or organization)                  Identification No.)


                         12001 North Houston Rosslyn
                           Houston, Texas   77086
                  (Address of principal executive offices)

                               (281) 447-8787
            (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


As of May 12, 1998 there were 28,515,153 shares of the Company's common stock,
$0.001 par value, outstanding.
<PAGE>   2
                           HANOVER COMPRESSOR COMPANY
                           CONSOLIDATED BALANCE SHEET
                            (IN THOUSANDS OF DOLLARS)

<TABLE>
<CAPTION>   
                                                                           March 31, 1998    December 31,
                             ASSETS                                           (unaudited)         1997
                                                                           -------------     ------------
<S>                                                                     <C>                  <C>      
Current assets:
      Cash and cash equivalents                                            $     14,553      $      4,561
      Accounts receivable, net                                                   46,608            41,041
      Inventory                                                                  36,492            32,860
      Costs and estimated earnings in excess of billings
           on uncompleted contracts                                               6,204             6,658
      Prepaid taxes                                                               6,928             6,919
      Other current assets                                                        7,299             2,750
                                                                           ------------      ------------

           Total current assets                                                 118,084            94,789
                                                                           ------------      ------------

Property, plant and equipment:
      Compression equipment                                                     467,150           438,351
      Land and buildings                                                         11,027            10,544
      Transportation and shop equipment                                          15,362            14,589
      Other                                                                       7,478             6,824
                                                                           ------------      ------------
                                                                                501,017           470,308
      Accumulated depreciation                                                  (84,726)          (76,238)
                                                                           ------------      ------------
           Net property, plant and equipment                                    416,291           394,070
                                                                           ------------      ------------

Intangible and other assets                                                      18,725            17,593
                                                                           ============      ------------

                                                                           $    553,100      $    506,452
                                                                           ============      ============

           LIABILITIES AND STOCKHOLDERS' EQUITY

Current liabilities:
      Current maturities of long-term debt                                 $      1,782      $      2,222
      Accounts payable, trade                                                    19,065            16,219
      Accrued liabilities                                                        10,181             9,088
      Advance billings                                                            7,353             6,752
      Billings on uncompleted contracts in excess of
        costs and estimated earnings                                              3,397             2,481
                                                                           ------------      ------------

           Total current liabilities                                             41,778            36,762

Long-term debt                                                                  190,855           158,838
Other obligations                                                                   893               899
Deferred income taxes                                                            25,195            21,682
                                                                           ------------      ------------

           Total liabilities                                                    258,721           218,181
                                                                           ------------      ------------

Commitments and contingencies

Stockholders' equity:
      Common stock, $.001 par value; 100 million shares authorized;
           28,510,570 (unaudited) and 28,367,169 shares issued,
           respectively                                                              29                28
      Additional paid-in capital                                                268,431           268,588
      Notes receivable - employee stockholders                                  (10,735)          (10,748)
      Retained earnings                                                          36,872            30,621
      Treasury stock - 31,347 common shares, at cost                               (218)             (218)
                                                                           ------------      ------------

           Total stockholders' equity                                           294,379           288,271
                                                                           ------------      ------------

                                                                           $    553,100      $    506,452
                                                                           ============      ============
</TABLE>

          See accompanying notes to consolidated financial statements 


<PAGE>   3
                           HANOVER COMPRESSOR COMPANY
                        CONSOLIDATED STATEMENT OF INCOME
                                   (UNAUDITED)
                    (IN THOUSANDS, EXCEPT PER SHARE AMOUNTS)

<TABLE>
<CAPTION>
                                                  Three months
                                                 ended March 31,
                                                ----------------
                                                1998       1997
                                              -------     -------
<S>                                           <C>         <C>    
Revenues:
      Rentals and maintenance                 $35,172     $24,320
      Compressor fabrication                   16,284       7,527
      Production equipment fabrication          8,958       8,671
      Other                                     1,035         406
                                              -------     -------
                                               61,449      40,924
                                              -------     -------
Expenses:
      Rentals and maintenance                  13,284       9,455
      Compressor fabrication                   13,733       6,359
      Production equipment fabrication          6,021       5,990
      Selling, general and administrative       6,048       4,694
      Depreciation and amortization             9,114       6,245
      Interest expense                          3,085       2,571
                                              -------     -------
                                               51,285      35,314
                                              -------     -------
Income before income taxes                     10,164       5,610
Provision for income taxes                      3,913       2,216
                                              -------     -------
Net income                                    $ 6,251     $ 3,394
                                              =======     =======



Weighted average common
      equivalent shares outstanding:
      Basic                                    28,462      22,910
                                              -------     -------
      Diluted                                  30,003      24,465
                                              -------     -------

Earnings per common share:
      Basic                                   $  0.22     $  0.15
                                              -------     -------
      Diluted                                 $  0.21     $  0.14
                                              -------     -------
</TABLE>

          See accompanying notes to consolidated financial statements.

<PAGE>   4

                           HANOVER COMPRESSOR COMPANY
                      CONSOLIDATED STATEMENT OF CASH FLOWS
                                   (UNAUDITED)
                            (IN THOUSANDS OF DOLLARS)


<TABLE>
<CAPTION>
                                                                        Three months 
                                                                       ended March 31,
                                                                       ---------------
                                                                     1998            1997
                                                                  ----------      ----------
<S>                                                               <C>             <C>       
Cash flows from operating activities:
     Net income                                                   $    6,251      $    3,394
     Adjustments:
         Depreciation and amortization                                 9,114           6,244
         Amortization of debt issuance and debt discount                 182             251
         Gain on sale of assets                                         (747)            (52)
         Deferred income taxes                                         3,513           1,827
         Changes in assets and liabilities:
              Accounts receivable                                     (5,567)         (1,867)
              Inventory                                               (3,632)         (7,745)
              Costs and estimated earnings versus billings on
                  uncompleted contracts                                1,370           5,975
              Accounts payable and other liabilities                   3,933          10,295
              Advance billings                                           601            (881)
              Other                                                   (4,558)         (3,208)
                                                                  ----------      ----------

Net cash provided by operating activities                             10,460          14,233

Cash flows from investing activities:
     Capital expenditures                                            (33,598)        (33,985)
     Proceeds from sale of fixed assets                                1,830             416
                                                                  ----------      ----------

Net cash used in investing activities                                (31,768)        (33,569)

Cash flows from financing activities:
     Net borrowings on revolving credit facility                      32,000          16,500
     Repayments of shareholder notes                                      13              --
     Equity issuance costs                                              (161)             --
     Cash received from exercise of stock options                          5              --
     Issuance of common stock                                             --              63
     Debt issuance costs                                                 (27)             --
     Repayment of long-term debt                                        (530)            (67)
     Other                                                                --              25
                                                                  ----------      ----------

Net cash provided by financing activities                             31,300          16,521
                                                                  ----------      ----------

Net increase/(decrease) in cash and cash equivalents                   9,992          (2,815)
Cash and cash equivalents at beginning of period                       4,561           7,322
                                                                  ----------      ----------

Cash and cash equivalents at end of period                        $   14,553      $    4,507
                                                                  ==========      ==========


Supplemental disclosure of cash flow information:
     Interest paid                                                $    2,444      $    1,168
     Income taxes paid                                            $       89      $      250
</TABLE>


          See accompanying notes to consolidated financial statements.

<PAGE>   5

                           HANOVER COMPRESSOR COMPANY

                   Notes to Consolidated Financial Statements


1.       BASIS OF PRESENTATION

       The accompanying unaudited consolidated financial statements of Hanover
Compressor Company (the "Company") included herein have been prepared in
accordance with generally accepted accounting principles for interim financial
information and in conjunction with the rules and regulations of the Securities
and Exchange Commission.  Accordingly, they do not include all of the
information and footnotes required by generally accepted accounting principles
for complete financial statements.  The Company believes, however, the
disclosures are adequate to make the information presented not misleading.  It
is the opinion of management that the information furnished includes all
adjustments, consisting only of normal recurring adjustments, which are
necessary to present fairly the financial position, results of operations, and
cash flows of the Company for the periods indicated.  It is suggested the
financial statement information included herein be read in conjunction with the
consolidated financial statements and notes thereto included in the Company's
Annual Report on Form 10-K for the year ended December 31, 1997.  These interim
results are not necessarily indicative of results for a full year.

         EARNINGS PER COMMON SHARE

           The Company adopted Statement of Financial Accounting Standard No.
128 (FAS 128), "Earnings Per Share," beginning with the Company's fourth
quarter of 1997.  All prior period earnings per share data have been restated
to conform to the provisions of this statement. Basic earnings per common share
is computed using the weighted average number of shares outstanding for the
period. Diluted earnings per common share is computed using the weighted
average number of shares outstanding adjusted for the incremental shares
attributed to outstanding options and warrants to purchase common stock.
Included in diluted shares are common stock equivalents relating to options of
1,098,000 and 986,000 and warrants of 443,000 and 569,000 for the three months
ended March 31, 1998 and 1997, respectively.

         OTHER COMPREHENSIVE INCOME

         The Company adopted Statement of Financial Standard No. 130 (FAS 130),
"Reporting Comprehensive Income," in the first quarter of 1998. For the three
months ended March 31, 1998 and 1997, there were no significant differences
between net income and comprehensive income.


2.       INVENTORIES

         Inventory consisted of the following amounts (in thousands):

<TABLE>                          
<CAPTION>                         
                                           March 31,      December 31,
                                             1998             1997
                                          -----------     ------------
                                          (unaudited)   
         <S>                              <C>             <C>
         Parts and supplies               $    22,357     $     20,141
         Work in progress                       8,875            8,766
         Finished goods                         5,260            3,953
                                          -----------     ------------
                                          $    36,492     $     32,860
                                          ===========     ============
</TABLE>                         

<PAGE>   6
3.       COMMITMENTS AND CONTINGENCIES

         In the ordinary course of business the Company is involved in various
pending or threatened legal actions.  While management is unable to predict the
ultimate outcome of these actions, it believes that any ultimate liability
arising from these actions will not have a material adverse effect on the
Company's consolidated financial position or operating results.
<PAGE>   7
ITEM 2. MANAGEMENT'S DISCUSSION AND ANALYSIS OF FINANCIAL CONDITION AND RESULTS
        OF OPERATIONS

SPECIAL NOTE REGARDING FORWARD-LOOKING STATEMENTS

         Certain matters discussed in this document are "forward-looking
statements" intended to qualify for the safe harbors from liability established
by the Private Securities Litigation Reform Act of 1995.  These forward-looking
statements can generally be identified as such because the context of the
statement will include words such as the Company "believes", "anticipates",
"expects", "estimates" or words of similar import.  Similarly, statements that
describe the Company's future plans, objectives or goals are also
forward-looking statements.  Such forward-looking statements are subject to
certain risks and uncertainties which could cause actual results to differ
materially from those anticipated as of the date of this report.  The risks and
uncertainties include (1) the loss of market share through competition, (2) the
introduction of competing technologies by other companies, (3) a prolonged
substantial reduction in natural gas prices which would cause a decline in the
demand for the Company's compression and oil and gas production equipment, (4)
new governmental safety, health and environmental regulations which could
require significant capital expenditures by the Company and (5) changes in
economic or political conditions in the countries in which the Company
operates.  The forward-looking statements included herein are only made as of
the date of this report and the Company undertakes no obligation to publicly
update such forward-looking statements to reflect subsequent events or
circumstances.

GENERAL

         The Company is a leading provider of a broad array of natural gas
compression rental, operations and maintenance services in the United States
and select international markets.  The Company's operations consist of
providing gas compression services through renting, maintaining and operating
natural gas compressors and engineering, fabricating and selling gas
compression and oil and gas production equipment.  As of March 31, 1998, the
Company had a fleet of 2,183 compression rental units with an aggregate
capacity of approximately 823,000 horsepower.  The Company's products and
services are essential to the production, transportation, processing and
storage of natural gas and are provided primarily to energy producers and
processors.

RESULTS OF OPERATIONS

THREE MONTHS ENDED MARCH 31, 1998 COMPARED TO THREE MONTHS ENDED MARCH 31, 1997

REVENUES

         The Company's total revenues increased by $20.5 million, or 50%, to
$61.4 million during the three months ended March 31, 1998 from $40.9 million
during the three months ended March 31, 1997. The increase resulted both from
growth of the Company's natural gas compressor rental fleet as well as
increased demand for both compressor equipment and production equipment
fabrication.

         Revenues from rentals and maintenance increased by $10.9 million, or
45%, to $35.2 million during the three months ended March 31, 1998 from $24.3
million during the three months ended March 31, 1997.  Domestic revenues from
rentals and maintenance increased by $7.7 million, or 38%, to $27.7 million
during the three months ended March 31, 1998 from $20.0 million during the
three months ended March 31, 1997.  International revenues from rentals and
maintenance increased by $3.2 million, or 77%, to $7.5 million during the three
months ended March 31, 1998 from $4.3 million during the three months ended
March 31, 1997.  The increase in both domestic and international rental and
maintenance revenues resulted primarily from expansion of the Company's rental
fleet.  Domestic horsepower in the rental fleet increased by 27% from
approximately 535,000 horsepower at March 31, 1997 to approximately 676,000
horsepower at March 31, 1998.  In addition, international horsepower increased
by 113% from approximately 69,000 horsepower at March 31, 1997 to approximately
147,000 horsepower at March 31, 1998.

         Revenues from the fabrication and sale of compressor equipment to
third parties increased by $8.8 million, or 116%, to $16.3 million during the
three months ended March 31, 1998 from $7.5 million during the three months
ended March 31, 1997.  During the three
<PAGE>   8
months ended March 31, 1998, an aggregate of approximately 55,000 horsepower of
compression equipment was fabricated, 43% of which was placed in the rental
fleet and 57% of which was sold to third party customers.  During the three
months ended March 31, 1997, approximately 38,000 horsepower was fabricated, 59%
of which was placed in the Company's rental fleet and 41% of which was sold to
third party customers.  The increase in horsepower produced resulted from
increased demand in the overall natural gas compression market.  In addition,
the increase in compressor equipment fabrication revenue resulted from a shift
in production of compression equipment for the Company's rental fleet to
production of such equipment for sale to third parties for the three months
ended March 31, 1998 as compared to the three months ended March 31, 1997.  The
Company believes that this shift is not indicative of any future period
performance as this blend of rentals and sales will vary from period to period
based upon the Company's needs as well as market conditions.

         Revenues from the fabrication and sale of production equipment
increased by $0.3 million, or 3%, to $9.0 million during the three months ended
March 31, 1998 from $8.7 million during the three months ended March 31, 1997.

EXPENSES

         Rentals and maintenance operating expenses increased by $3.8 million,
or 41%, to $13.3 million during the three months ended March 31, 1998 from $9.5
million during the three months ended March 31, 1997.  The increase results
primarily from the corresponding 45% increase in revenues from rentals and
maintenance during the three months ended March 31, 1998 over the corresponding
period in 1997.

         Operating expenses of compressor fabrication increased by $7.4
million, or 116%, to $13.7 million during the three months ended March 31, 1998
from $6.4 million during the three months ended March 31, 1997.  This expense
increase was a result of the corresponding increase in compressor fabrication
revenue.  There was no change in operating expenses attributable to production
equipment fabrication, which was $6.0 million during the three months ended
March 31, 1998 and March 31, 1997 and approximates the 3% increase in
production equipment revenue.

         Selling, general and administrative expenses increased $1.3 million,
or 29%, to $6.0 million during the three months ended March 31, 1998 from $4.7
million during the three months ended March 31, 1997.  The increase in these
expenses resulted from the increased activity in the Company's rental and
maintenance and compressor fabrication business segments as described above.

         Depreciation and amortization increased by $2.9 million, or 46%, to
$9.1 million during the three months ended March 31, 1998 from $6.2 million
during the three months ended March 31, 1997.  The increase resulted from
expansion of the rental fleet and other capital expenditures which increased the
amount invested in property, plant and equipment from approximately $348 million
at March 31, 1997 to approximately $501 million at March 31, 1998.

INTEREST EXPENSE

         Interest expense increased by $0.5 million, or 20%, to $3.1 million
during the three months ended March 31, 1998 from $2.6 million during the three
months ended March 31, 1997.  The interest expense increase resulted from new
indebtedness incurred to finance the capital expenditures for property, plant 
and equipment.

<PAGE>   9
INCOME TAXES

         The provision for income taxes increased by $1.7 million, or 77%, to
$3.9 million during the three months ended March 31, 1998 from $2.2 million
during the three months ended March 31, 1997.  The increase resulted primarily
from the corresponding increase in income before taxes.  The effective income
tax rate during the three months ended March 31, 1998 and 1997 was 38.5% and
39.5% respectively.

NET INCOME

         Net income increased $2.9 million, or 84%, to $6.3 million during the
three months ended March 31, 1998 from $3.4 million during the three months
ended March 31, 1997 for the reasons discussed above. 

LIQUIDITY AND CAPITAL RESOURCES

         The Company has historically utilized internally generated funds and
equity and debt financing to finance the growth of its compressor fleet and
maintain sufficient compression and production equipment inventory.  Cash flows
from operating activities, before changes in assets and liabilities, were $18.3
million for the three months ended March 31, 1998 as compared to $11.7 million
for the three months ended March 31, 1997.  Capital expenditures for property,
plant and equipment were $33.6 million for the three months ended March 31,
1998 as compared to $34.0 million for the three month period ended March 31,
1997.  Inventory increased $3.6 million during the three months ended March 30,
1998 due to increases in compressor and production equipment fabrication
operations and compression rental operations.  Bank borrowings were $32.0
million for the three months ended March 31, 1998 as compared to $16.5 million
for the three months ended March 31, 1997.

         The Company has Subordinated Notes outstanding in the aggregate
principal amount of $23.5 million, bearing interest at 7%, payable
semi-annually, with principal due on December 31, 2000.  As of March 31, 1998,
the Company has approximately $37 million of credit capacity remaining on its
$200 million credit facility with the Chase Manhattan Bank, as agent.  In order
to fund its anticipated level of 1998 capital expenditures, the Company
anticipates arranging additional sources of debt and/or equity in 1998

IMPACT OF THE YEAR 2000

         The Company plans to install various modifications to existing
computer software during 1998 to include, among other things, an accommodation
of the problems associated with computer programs reflecting the year 2000. The
costs associated with the software modifications are not expected to be
material in relation to either future operating results or financial condition.

         The Company has not initiated formal communications with all of its
significant suppliers and vendors to ensure that those parties have appropriate
plans to address year 2000 issues where they may otherwise impact the
operations of the Company; however, the Company does not have any significant
suppliers or vendors that directly interface with the Company's information
technology systems. There is no guarantee that the systems of other companies
on which the Company relies will be converted timely and will not have an
adverse effect on the Company.
<PAGE>   10

ITEM 6.  EXHIBITS AND REPORTS ON FORM 8-K

(a)      Exhibits

         27       Financial Data Schedule

(b)      Reports Submitted on Form 8-K;  none.

All other items specified by Part II of this report are inapplicable and have
been omitted.
<PAGE>   11
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.

HANOVER COMPRESSOR COMPANY
Date:  May 12, 1998
By:

/s/ Michael J. McGhan  
-------------------------
Michael J. McGhan
President and Chief Executive Officer

Date: May 12, 1998
By:

/s/ Curtis A. Bedrich  
-------------------------
Curtis A. Bedrich
Chief Financial Officer

<PAGE>   12

                              INDEX TO EXHIBITS
<TABLE>
<CAPTION>
EXHIBIT 
NUMBER        DESCRIPTION
-------       -----------
<S>           <C>
  27          Financial Data Schedule
</TABLE>