FILED PURSUANT TO RULE 424(B)(3)
                                                      REGISTRATION NO. 333-51430

                     SUPPLEMENT NO. 1 DATED MARCH 22, 2001
                      TO PROSPECTUS DATED JANUARY 3, 2001
                        RELATING TO 2,303,294 SHARES OF
                                COMMON STOCK OF
                           HANOVER COMPRESSOR COMPANY

NOTICE:  Certain information set forth on page 12 of this prospectus has been
amended as follows.  The number of shares set forth opposite the name of Charles
Dean Guthrie in the columns entitled "Number of Shares of Common Stock Owned
Prior to the Offering" and "Number of Shares of Common Stock Offered Hereby" has
been changed from 247 to 1,147.