<PAGE>   1
  As filed with the Securities and Exchange Commission on July 27, 1999

                                           Registration No 333-________


                       SECURITIES AND EXCHANGE COMMISSION
                             WASHINGTON, D.C. 20549


                                    FORM S-8
                          REGISTRATION STATEMENT UNDER
                           THE SECURITIES ACT OF 1933


                              MESA AIR GROUP, INC.
             (Exact name of registrant as specified in its charter)

<TABLE>
<S>                                                          <C>
             Nevada                                              85-0302351
(State or other jurisdiction of                               (I.R.S. Employer
incorporation or organization)                               Identification No.)

410 North 44th Street, Suite 700, Phoenix, Arizona                       85008
(Address of Principal Executive Offices)                              (Zip Code)
</TABLE>

      Mesa Air Group, Inc. Restated and Amended Employee Stock Option Plan
                            (Full title of the plan)


     Corporation Trust Co. of Nevada, One East First Street, Reno, NV 89501
                     (Name and address of agent for service)

                                 (602) 685-4000
          (Telephone number, including area code, of agent for service)


                         CALCULATION OF REGISTRATION FEE

<TABLE>
<CAPTION>
                                                        PROPOSED               PROPOSED
        TITLE OF                                        MAXIMUM                MAXIMUM
       SECURITIES                 AMOUNT                OFFERING              AGGREGATE             AMOUNT OF
          TO BE                   TO BE                  PRICE                 OFFERING            REGISTRATION
      REGISTERED(1)             REGISTERED            PER UNIT(2)              PRICE(2)                FEE
      -------------             ----------            -----------              --------                ---
<S>                             <C>                   <C>                   <C>                     <C>
Common Stock                    1,250,000                $7.88              $9,580,000.00           $2,738.30
</TABLE>

(1)  This Registration Statement registers additional shares to be offered by
     the Registrant pursuant to its 1996 Employee Stock Option Plan.

(2)  Estimated solely for the purpose of calculating the amount of the
     registration fee, pursuant to Rules 457(c) and 457(h) of the Securities Act
     of 1933, as amended on the basis of the average of the high and low prices
     for shares of Common Stock on July 23, 1999.
<PAGE>   2
         This Registration Statement is filed pursuant to General Instruction E
of Form S-8 for the purpose of registering additional shares of Common Stock, no
par value, of Mesa Air Group, Inc., a Nevada corporation, for Mesa Air's 1996
Employee Stock Option Plan.

          INCORPORATION BY REFERENCE OF EARLIER REGISTRATION STATEMENT

         The Registration Statement on Form S-8 (Registration No. 333-02791),
previously filed with the Securities and Exchange Commission, is incorporated
herein by reference.
<PAGE>   3
                                   SIGNATURES


         Pursuant to the requirements of the Securities Act of 1933, as amended,
the registrant certifies that it has reasonable grounds to believe that it meets
all of the requirements for filing on Form S-8 and has duly caused this
registration statement to be signed on its behalf by the undersigned, thereunto
duly authorized, in the City of Phoenix, State of Arizona, on July 23, 1999.

                                        MESA AIR GROUP, INC.



                                        By:      /s/ Jonathan G. Ornstein
                                                --------------------------------
                                                 Jonathan G. Ornstein, President
                                                 And Chief Executive Officer




                                        By:      /s/ Blaine M. Jones
                                                --------------------------------
                                                 Blaine M. Jones
                                                 Chief Financial Officer



                            SPECIAL POWER OF ATTORNEY

         KNOW ALL MEN BY THESE PRESENTS, that each of the undersigned
constitutes and appoints Jonathan G. Ornstein and Blaine M. Jones, and each of
them, his true and lawful attorney-in-fact and agent with full power of
substitution and resubstitution, for him and in his name, place and stead, in
any and all capacities, to sign any and all amendments (including post-effective
amendments) to this Form S-8 Registration Statement, and to file the same with
all exhibits thereto, and all documents in connection therewith, with the
Securities and Exchange Commission, granting such attorneys-in-fact and agents,
and each of them, full power and authority to do and perform each and every act
and thing requisite and necessary to be done in and about the premises, as fully
and to all intents and purposes as he might or could do in person, hereby
ratifying and confirming all that such attorneys-in-fact and agents, or each of
them, may lawfully do or cause to be done by virtue hereof.
<PAGE>   4
         Pursuant to the requirements of the Securities Act of 1933, this
Registration statement has been signed below by the following persons in the
capacities and on the date indicated.


<TABLE>
<CAPTION>
  Signature                                    Title                                                          Date
  ---------                                    -----                                                          ----
<S>                                            <C>                                                       <C>
                                               President, Chief Executive Officer and Chairman of
  /s/ Jonathan G. Ornstein                     the Board (Principal Executive Officer)                   July 23, 1999
  ---------------------------------
  Jonathan G. Ornstein


  /s/ Blaine M. Jones                          Chief Financial Officer and Treasurer (Principal          July 23, 1999
  ---------------------------------            Financial Officer)
  Blaine M. Jones

  /s/ Paul R. Madden
  ---------------------------------            Director                                                  July 23, 1999
  Paul R. Madden

  /s/ James E. Swigert
  ---------------------------------            Director                                                  July 23, 1999
  James E. Swigert

  /s/ Daniel J. Altobello
  ---------------------------------            Director                                                  July 23, 1999
  Daniel J. Altobello

  /s/ Jack Braly
  ---------------------------------            Director                                                  July 23, 1999
  Jack Braly

  /s/ Herbert A. Denton
  ---------------------------------            Director                                                  July 23, 1999
  Herbert A. Denton

  /s/ General Ronald R. Fogelman
  ---------------------------------            Director                                                  July 23, 1999
  General Ronald R. Fogelman

  /s/ Maurice A. Parker
  ---------------------------------            Director                                                  July 23, 1999
  Maurice A. Parker

  /s/ Larry L. Risley
  ---------------------------------            Director                                                  July 23, 1999
  Larry L. Risley

  /s/ George Murnane, III
  ---------------------------------            Director                                                  July 23, 1999
  George Murnane, III
</TABLE>
<PAGE>   5
                                  EXHIBIT INDEX

<TABLE>
<CAPTION>
Exhibit
Number              Description
------              -----------
<S>                 <C>
   4                Restated and Amended Employee Stock Option Plan

   5                Form of opinion rendered by Squire, Sanders & Dempsey
                    L.L.P., counsel for the Registrant

   23               Consent of Squire, Sanders & Dempsey L.L.P. (Included in Exhibit 5)
</TABLE>