<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)


             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)

            Mesa Air Group, Inc. Outside Directors' Stock Option Plan
                            (Full title of the plan)


    CT 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               REGISTERED            PER UNIT(1)              PRICE(1)                FEE
<S>                             <C>                   <C>                   <C>                    <C>
      Common Stock               150,000                 $7.88              $1,182,000.00            $328.60
</TABLE>




 (1) 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
                                     PART II

               INFORMATION REQUIRED IN THE REGISTRATION STATEMENT


ITEM 3.           INCORPORATION OF CERTAIN DOCUMENTS BY REFERENCE.

         The following documents are hereby incorporated by reference herein and
shall be deemed a part hereof:

         (a) The Annual Report of Mesa Air Group, Inc. ("Mesa") on Form 10-K for
the fiscal year ended September 30, 1998, filed pursuant to Section 13(a) or
15(d) of the Securities Exchange Act of 1934, as amended (the "Exchange Act");

         (b) All reports filed by Mesa with the Securities and Exchange
Commission pursuant to Section 13(a) or 15(d) of the Exchange Act since
September 30, 1998; and

         (c) The description of Mesa's capital stock contained in its
Registration Statement on Form 8-A filed with the Securities and Exchange
Commission pursuant to Section 12 of the Exchange Act of 1934.

         All documents subsequently filed by Mesa pursuant to Sections 13(a), 14
or 15(d) of the Exchange Act, prior to the filing of a post-effective amendment
to this Registration Statement which indicates that all securities offered have
been sold or which deregisters all securities then remaining unsold, shall be
deemed to be incorporated by reference in this Registration Statement and to be
a part hereof from the date of filing such documents.

         Any statement contained in a document incorporated or deemed to be
incorporated by reference herein shall be deemed to be modified or superseded
for purposes of this Registration Statement to the extent that a statement
contained herein or in any other subsequently filed document which also is or is
deemed to be incorporated by reference herein modifies or supersedes such
statement. Any such statement so modified or superseded shall not be deemed,
except as so modified or superseded, to constitute a part of this Registration
Statement.

ITEM 4.           DESCRIPTION OF SECURITIES.  Not applicable.

ITEM 5.           INTERESTS OF NAMED EXPERTS AND COUNSEL.  Not applicable.

ITEM 6.           INDEMNIFICATION OF DIRECTORS AND OFFICERS.

         The Registrant's Articles of Incorporation and Bylaws require the
Registrant to indemnify its directors and officers and to the fullest extent
provided by Nevada law.

         The Registrant currently maintains directors' and officers' liability
insurance.

ITEM 7.           EXEMPTION FROM REGISTRATION CLAIMED.  Not applicable.


<PAGE>   3
ITEM 8.           EXHIBITS.

         Exhibit Index located at Page 10.

ITEM 9.           UNDERTAKINGS.

         (a)      The undersigned registrant hereby undertakes:

                  (1) To file, during any period in which offers or sales are
being made, a post-effective amendment to this registration statement:

                           (i)      To include any  prospectus  required by
         Section 10(a)(3) of the Securities Act of 1933;

                           (ii) To reflect in the prospectus any facts or events
         arising after the effective date of the registration statement (or the
         most recent post-effective amendment thereof) which, individually or in
         the aggregate, represents a fundamental change in the information set
         forth in the registration statement. Notwithstanding the foregoing, any
         increase or decrease in volume of securities offered (if the total
         dollar value of securities offered would not exceed that which was
         registered) and any deviation from the low or high end of the estimated
         maximum offering range may be reflected in the form of prospectus filed
         with the Commission pursuant to Rule 424(b) if, in the aggregate, the
         changes in volume and price represent no more than a 20 percent change
         in the maximum aggregate offering price set forth in the "Calculation
         of Registration Fee" table in the effective registration statement;

                           (iii) To include any material information with
         respect to the plan of distribution not previously disclosed in the
         registration statement or any material change to such information in
         the registration statement;

                  (2) That, for the purposes of determining any liability under
the Securities Act of 1933, each such post-effective amendment shall be deemed
to be a new registration statement relating to the securities offered therein,
and the offering of such securities at that time shall be deemed to be the
initial bona fide offering thereof.

                  (3) To remove from registration by means of a post-effective
amendment any of the securities being registered which remain unsold at the
termination of the offering.

         (b) The undersigned Registrant hereby undertakes that, for purposes of
determining any liability under the Securities Act of 1933, each filing of the
Registrant's annual report pursuant to Section 13(a) or Section 15(d) of the
Securities Act of 1934 (and, where applicable, each filing of an employee
benefit plan's annual report pursuant to Section 15(d) of the Securities
Exchange Act of 1934) that is incorporated by reference in the registration
statement shall be deemed to be a new registration statement relating to the
securities offered therein, and
<PAGE>   4
the offering of such securities at that time shall be deemed to be the initial
bona fide offering thereof.

         (c) Insofar as indemnification for liabilities arising under the
Securities Act of 1933 may be permitted to directors, officers and controlling
persons of the registrant pursuant to the foregoing provisions, or otherwise,
the registrant has been advised that in the opinion of the Securities and
Exchange Commission such indemnification is against public policy as expressed
in the Act and is, therefore, unenforceable. In the event that a claim for
indemnification against such liabilities (other than the payment by the
registrant of expenses incurred or paid by a director, officer or controlling
person of the registrant in the successful defense of any action, suit or
proceeding) is asserted by such director, officer or controlling person in
connection with the securities being offered, the registrant will, unless in the
opinion of its counsel the matter has been settled by controlling precedent,
submit to a court of appropriate jurisdiction the question of whether such
indemnification by it is against public policy as expressed in the Act and will
be governed by the final adjudication of such issue.





<PAGE>   5
                                   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 3, 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>   6
         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>
/s/ Jonathan G. Ornstein
------------------------
    Jonathan G. Ornstein                       President, Chief Executive Officer and Chairman of
                                               the Board (Principal Executive Officer)                   July 23, 1999



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


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


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


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


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


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


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


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


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


/s/ George Murnane, III
------------------------
  George Murnane, III                          Director                                                  July 23, 1999

</TABLE>


<PAGE>   7
                                  EXHIBIT INDEX


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

4        Mesa Air Group, Inc. Outside Directors' 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)