<Page>

                                                                   Exhibit 10.13

                                                                  EXECUTION COPY
                                                                  --------------

                            STOCK PURCHASE AGREEMENT

                  STOCK PURCHASE AGREEMENT dated as of December 19, 2001 between
the persons set forth in Schedule A hereto (each a "Seller" and collectively the
"Sellers") and Hawaiian Airlines, Inc., a Hawaii corporation ("Purchaser"). All
capitalized terms used but not otherwise defined herein shall have the meaning
ascribed to such terms in the Merger Agreement (as defined below).

                  WHEREAS concurrently herewith Purchaser is entering into a
merger agreement dated as of the date hereof by and among Purchaser, Aloha
Airgroup, Inc. (the "Company"), TurnWorks Acquisition III, Inc., and TurnWorks,
Inc. (the "Merger Agreement"); and

                  WHEREAS the Merger Agreement requires the Sellers to sell to
Purchaser an aggregate of 5,000 shares (the "Shares") of issued and outstanding
Series C 10% exchangeable preferred stock, stated value U.S.$1,000 per share, of
the Company and Purchaser to purchase from the Sellers the Shares, upon the
terms and subject to the conditions set forth herein;

                  NOW, THEREFORE, in consideration of the premises and the
mutual agreements and covenants hereinafter set forth, each of the Sellers and
Purchaser hereby agree as follows:

         1. SALE OF SHARES. Subject to the terms and conditions contained
herein, each Seller will sell to Purchaser, and Purchaser will buy from such
Seller, the Shares set forth opposite such Seller's name in Schedule A hereto
for an aggregate cash purchase price of U.S.$5,000,000 (the "Purchase Price"),
representing U.S.$1,000 per Share, payable at the Closing Time (as defined
below).

         2. CLOSING.

            (a) The closing of the sale and purchase under Section 1 of this
Agreement shall take place at the offices of Cleary, Gottlieb, Steen & Hamilton,
One Liberty Plaza, New York, New York 10006-1470, on the same day as, and
immediately prior to, the Effective Time (as defined in the Merger Agreement)
(the "Closing Time").

            (b) At the Closing Time, the Sellers shall deliver or cause to be
delivered to Purchaser (i) stock certificates evidencing the Shares duly
endorsed in blank or accompanied by a duly executed stock power in proper form
for transfer and (ii) a receipt for the Purchase Price in respect of the Shares.

            (c) At the Closing Time, Purchaser shall deliver to the Sellers (i)
U.S.$3,750,000 to Aloha Securities & Investment Co. and U.S.$1,250,000 to
Sheridan Ing Partners Hawaii, as payment in full of the Purchase Price and (ii)
a receipt for the Shares. Payment of the Purchase Price shall be made by either
(A) certified checks or (B) wire transfer of immediately available funds to the
bank account of each Seller, as furnished to Purchaser in writing not less than
two business days prior to the Closing Time.


<Page>

         3. REPRESENTATIONS OF THE SELLERS. As an inducement to Purchaser to
enter into this Agreement, each Seller represents and warrants to Purchaser
that:

            (a) Such Seller owns beneficially and of record the Shares and has
good and valid title to the Shares, free and clear of all Liens. Such Seller has
the unrestricted power and authority to transfer the Shares to Purchaser. The
delivery of and payment for the Shares pursuant to this Agreement will transfer
to Purchaser good and valid title to such Seller's Shares free and clear of any
perfected security interest or any other security interests, claims, liens or
encumbrances. There are no voting trusts, stockholder agreements, proxies or
other agreements or understandings in effect with respect to the voting or
transfer of any of such Seller's Shares.

            (b) Such Seller has all requisite power and authority to enter into
and perform its obligations under this Agreement and to consummate the
transactions contemplated hereby; and the execution and delivery of this
Agreement by such Seller, the performance by such Seller of its obligations
hereunder and the consummation by such Seller of the transactions contemplated
hereby have been duly authorized by all requisite action on the part of such
Seller.

            (c) This Agreement has been duly executed and delivered by such
Seller and constitutes a legal, valid and binding obligation of such Seller,
enforceable against such Seller in accordance with its terms, except (i) as
limited by applicable bankruptcy, insolvency, reorganization, moratorium,
fraudulent conveyance and other similar laws of general application affecting
enforcement of creditors' rights generally and (ii) the availability of the
remedy of specific performance or injunctive or other forms of equitable relief
may be subject to equitable defenses and would be subject to the discretion of
the court before which any proceeding therefor may be brought.

            (d) (i) No Order has been issued by any court or other Governmental
Authority against such Seller purporting to enjoin or restrain the execution,
delivery or performance of this Agreement; and (ii) as of the date hereof, there
is no litigation, suit, claim, action or proceeding pending or, to the knowledge
of such Seller, threatened in writing against such Seller or any of its property
or assets, before any court, arbitrator or Governmental Authority, domestic or
foreign, seeking relief which, if ordered, would delay or prevent the
consummation of the transaction contemplated hereby.

            (e) The execution, delivery and performance by such Seller of this
Agreement and the transactions contemplated hereby and thereby, including,
without limitation, the sale of the Shares by such Seller (i) if applicable, do
not contravene the terms of the articles of incorporation or by-laws, or similar
instrument of organization, or any amendment thereof, of such Seller, (ii) do
not violate, conflict with or result in any breach, default or contravention of
(or with due notice or lapse of time or both would result in any breach, default
or contravention of), or the creation of any Lien under, any contract,
indenture, mortgage, deed of trust, loan or credit agreement, note, lease or
other agreement or instrument (collectively, a "Contractual Obligation") of such
Seller, or any law, statute, rule or regulation (collectively, a "Requirement of
Law") applicable to such Seller and (iii) do not violate any Orders against, or
binding upon, such Seller.



                                       2
<Page>

            (f) No approval, consent, compliance, exemption, authorization or
other action by, or notice to, or filing with, any Governmental Authority or any
other Person, and no lapse of a waiting period under a Requirement of Law, is
necessary or required in connection with the execution, delivery or performance
(including, without limitation, the sale and delivery of the Shares) by, or
enforcement against, such Seller of this Agreement and the transactions
contemplated hereby.

            (g) No form of general solicitation or general advertising was used
by such Seller or its representatives in connection with the sale of the Shares.

            (h) No broker, finder or investment banker is entitled to any
brokerage, finder's or other fee or commission in connection with the
transaction contemplated hereby based upon arrangements made by or on behalf of
the Sellers.

         4. REPRESENTATIONS OF PURCHASER. As an inducement to the Sellers to
enter into this Agreement, Purchaser represents and warrants to each Seller
that:

            (a) Purchaser is aware that the Shares may not be sold, transferred,
offered for sale, pledged, hypothecated or otherwise disposed of without
registration or qualification under the Securities Act of 1933, as amended (the
"Securities Act"), and any applicable state securities laws, except pursuant to
an exemption from such registration or qualification under the Securities Act
and any applicable state securities laws. Purchaser is aware that the Company
has no obligation to register the Shares for resale.

            (b) Purchaser is a corporation duly incorporated, validly existing
and in good standing under the laws of the State of Hawaii and has all requisite
power and authority to enter into and perform its obligations under this
Agreement and to consummate the transactions contemplated hereby; and the
execution and delivery of this Agreement by Purchaser, the performance by
Purchaser of its obligations hereunder and the consummation by Purchaser of the
transactions contemplated hereby have been duly authorized by all requisite
action on the part of Purchaser.

            (c) This Agreement has been duly executed and delivered by Purchaser
and constitutes a legal, valid and binding obligation of Purchaser, enforceable
against it in accordance with its terms, except (i) as limited by applicable
bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance and
other similar laws of general application affecting enforcement of creditors'
rights generally and (ii) the availability of the remedy of specific performance
or injunctive or other forms of equitable relief may be subject to equitable
defenses and would be subject to the discretion of the court before which any
proceeding therefor may be brought.

            (d) (i) No Order has been issued by any court or other Governmental
Authority against Purchaser purporting to enjoin or restrain the execution,
delivery or performance of this Agreement; and (ii) as of the date hereof, there
is no litigation, suit, claim, action or proceeding pending or, to the knowledge
of Purchaser, threatened in writing against Purchaser or any of its property or
assets, before any court, arbitrator or Governmental


                                       3
<Page>

Authority, domestic or foreign, seeking relief which, if ordered, would delay or
prevent the consummation of the transaction contemplated hereby.

            (e) The execution, delivery and performance by Purchaser of this
Agreement and the transactions contemplated hereby and thereby (i) do not
contravene the terms of the Certificate of Incorporation or the By-laws, (ii) do
not violate, conflict with or result in any breach, default or contravention of
(or with due notice or lapse of time or both would result in any breach, default
or contravention of), or the creation of any Lien under, any Contractual
Obligation of Purchaser or any Requirement of Law applicable to Purchaser, and
(iii) do not violate any Orders against, or binding upon, Purchaser.

            (f) No approval, consent, compliance, exemption, authorization or
other action by, or notice to, or filing with, any Governmental Authority or any
other Person, and no lapse of a waiting period under a Requirement of Law, is
necessary or required in connection with the execution, delivery or performance
by, or enforcement against, Purchaser of this Agreement and the transactions
contemplated hereby.

            (g) Purchaser acknowledges that it did not agree to purchase the
Shares as a result of any form of general solicitation or general advertising.

            (h) No broker, finder or investment banker is entitled to any
brokerage, finder's or other fee or commission in connection with the
transaction contemplated hereby based upon arrangements made by or on behalf of
Purchaser.

         5. COVENANTS.

            (a) Purchaser covenants with each of the Sellers that it shall hold
the Shares until cancelled as contemplated in the Merger Agreement.

            (b) Purchaser acknowledges that it is not entitled to and covenants
with each of the Sellers that it will not receive any dividends or other
distributions as holder of the Shares prior to the Effective Time.

         6. CONDITIONS TO CLOSING.

            (a) The obligation of Purchaser to purchase the Shares, to pay the
purchase price therefor at the Closing Time and to perform any other obligations
hereunder shall be subject to the satisfaction (or waiver by Purchaser) of the
following conditions on or before the Closing Time:

            (i) REPRESENTATIONS AND COVENANTS. The representations and
            warranties of the Sellers contained herein shall have been true and
            correct when made and (other than the representations and warranties
            set out in Section 3(d)(ii) hereof) shall be true and correct in all
            material respects as of the Closing Time with the same force and
            effect as though made on and as of the Closing Time. Each of the
            Sellers shall have performed and complied in all material respects
            with all covenants and agreements required hereby to be performed or
            complied with by the Sellers on or prior to the Closing Time. Each
            of the Sellers shall have


                                       4
<Page>

            delivered to Purchaser a certificate, dated the Closing Time and
            signed by an authorized representative of such Seller, to the
            foregoing effect.

            (ii) NO ORDERS. No Order shall have been issued or litigation
            initiated by any Governmental Authority to restrain or prohibit, or
            to obtain damages or a discovery order in respect of, this Agreement
            or the consummation of the transactions contemplated hereby.

            (iii) CONSENTS. All authorizations, consents, orders or approvals
            of, or declarations or filings with, or expiration of waiting
            periods imposed by, or notifications to, any Governmental Authority
            required by any Law in connection with the execution, delivery and
            performance of this Agreement shall have been obtained, filed,
            expired or given as of the Closing Time.

            (b) The obligations of each of the Sellers to sell the Shares and to
perform any other obligations hereunder shall be subject to the satisfaction (or
waiver by the Sellers) of the following conditions on or before the Closing
Time:

            (i) REPRESENTATIONS AND COVENANTS. The representations and
            warranties of Purchaser contained herein shall have been true and
            correct when made and (other than the representations and warranties
            set out in Section 4(d)(ii) hereof) shall be true and correct in all
            material respects as of the Closing Time with the same force and
            effect as though made on and as of the Closing Time. Purchaser shall
            have performed and complied in all material respects with all
            covenants and agreements required hereby to be performed or complied
            with by Purchaser on or prior to the Closing Time. Purchaser shall
            have delivered to the Sellers a certificate, dated the Closing Time
            and signed by an officer of Purchaser, to the foregoing effect.

            (ii) NO ORDERS. No Order shall have been issued or litigation
            initiated by any Governmental Authority to restrain or prohibit, or
            to obtain damages or a discovery order in respect of, this Agreement
            or the consummation of the transactions contemplated hereby.

            (iii) CONSENTS. All authorizations, consents, orders or approvals
            of, or declarations or filings with, or expiration of waiting
            periods imposed by, or notifications to, any Governmental Authority
            required by any Law in connection with the execution, delivery and
            performance of this Agreement shall have been obtained, filed,
            expired or given as of the Closing Time.

            (c) The obligations of Purchaser and each of the Sellers under this
Agreement are subject to the satisfaction or waiver of all of the conditions
listed in Article VIII of the Merger Agreement.

         7. TERMINATION.

            (a) This Agreement may be terminated as follows:



                                       5
<Page>

            (i) by mutual written consent of each of the Sellers and Purchaser;

            (ii) at the written election of Purchaser, in the event that the
            conditions set forth in Section 6(a) have not been fulfilled by the
            Closing Time or have become impossible of fulfillment prior to the
            Closing Time;

            (iii) at the written election of the Sellers, in the event that the
            conditions set forth in Section 6(b) have not been fulfilled by the
            Closing Time or have become impossible of fulfillment prior to the
            Closing Time; or

            (iv) At the written election of either Purchaser or the Sellers, in
            the event that the conditions set forth in Section 6(c) have not
            been fulfilled by the Closing Time or have become impossible of
            fulfillment prior to the Closing Time.

            (b) This Agreement shall immediately terminate (without the need for
any further action by any of the parties hereto) if the Merger Agreement is
terminated for any reason whatsoever.

            (c) In the event of the termination of this Agreement pursuant to
the provisions of this Section 7, this Agreement shall become void and have no
effect, without any liability on the part of any party hereto or its directors,
officers or stockholders in respect of this Agreement.

         8. GOVERNING LAW. This Agreement shall be governed by and construed in
accordance with the laws of the State of Delaware applicable to contracts
executed in and to be performed in that State, except to the extent that
provisions of the Hawaii Business Corporation Act, as amended, ("HBCA") are
mandatorily applicable. Each of the parties hereto (i) consents to submit itself
to the personal jurisdiction of any Delaware state court located in the city of
Wilmington if any dispute arises under this Agreement or any transaction
contemplated hereby, (ii) agrees that it will not attempt to deny or defeat such
personal jurisdiction by motion or other request for leave from any such court,
(iii) agrees that it will not bring any action, suit or proceeding relating to
this Agreement or any transaction contemplated hereby in any court other than
any such court, (iv) waives any right to trial by jury with respect to any
action, suit or proceeding related to or arising out of this Agreement or any
transaction contemplated hereby, (v) waives any objection to the laying of venue
of any action, suit or proceeding arising out this Agreement or any transaction
contemplated hereby in any such court, (vi) waives and agrees not to plead or
claim that any such action, suit or proceeding brought in any such court has
been brought in an inconvenient forum and (vii) agrees that a final judgment in
any such action, suit or proceeding in any such court shall be conclusive and
may be enforced in any other jurisdiction by suit on the judgment or in any
other manner provided by applicable law.

         9. ASSIGNMENT. This Agreement may not be assigned by any party hereto
without the prior written consent of the other parties hereto.

         10. PARTIES IN INTEREST. All the terms and provisions of this Agreement
shall be binding upon and inure to the benefit of and be enforceable by the
respective successors of the parties hereto.



                                       6
<Page>

         11. AMENDMENTS. This Agreement may be amended or modified only by an
instrument in writing signed by each of the Sellers and Purchaser.

         12. NOTICES. All notices, consents, requests, instructions, approvals
and other communications provided herein shall be validly given or made (and
shall be deemed to have been duly given or made upon receipt or delivery), if in
writing and delivered personally or sent by nationally recognized overnight
courier, by facsimile transmission (followed up by certified or registered mail,
return receipt requested) or by registered or certified mail return receipt
requested, (i) if to Purchaser at 3375 Koapaka Street, Suite G350, Honolulu, HI
96819-1869, attention: Vice Chairman and Chief Executive Officer, facsimile:
808-835-3688, with a copy to the attention of the General Counsel, facsimile:
808-835-3690 and (ii) if to the Sellers, to Aloha Securities & Investment
Company at 841 Bishop Street, Suite 940, Honolulu, HI, 96813, attention: Han P.
Ching, facsimile: 808-523-5600 and to Sheridan Ing Partners Hawaii at 841 Bishop
Street, Suite 860, Honolulu, HI 96813, attention: Richard K. M. Ing, facsimile:
808-531-2611.

         13. MISCELLANEOUS. This Agreement may be executed concurrently in two
or more counterparts, each of which shall be deemed an original, but all of
which together shall constitute one and the same instrument. Each counterpart
may be delivered by facsimile transmission, which transmission shall be deemed
delivery of an originally executed document.

         14. SEVERABILITY. If any one or more of the provisions contained
herein, or the application thereof in any circumstance, is held invalid, illegal
or unenforceable in any respect for any reason, the validity, legality and
enforceability of any such provision in every other respect and of the remaining
provisions hereof shall not be in any way impaired, unless the provisions held
invalid, illegal or unenforceable shall substantially impair the benefits of the
remaining provisions hereof; provided, however, that in no event shall Purchaser
be required to purchase the Shares if the Merger Agreement is terminated.

         15. ENTIRE AGREEMENT. This Agreement is intended by the parties as a
final expression of their understandings and is intended to be a complete and
exclusive statement of the agreement and understanding of the parties hereto in
respect of the subject matter contained herein. This Agreement supersedes all
prior agreements and understandings between the parties with respect to such
subject matter.

         16. FURTHER ACTION. Each of the parties hereto shall use all reasonable
efforts to take, or cause to be taken, all appropriate action, do or cause to be
done all things necessary, proper or advisable under applicable laws and
regulations, and execute and deliver such documents and other papers, as may be
required to carry out the provisions of, and consummate and make effective the
transactions contemplated by, this Agreement and the Merger Agreement.



                                       7
<Page>






                 REMAINDER OF THIS PAGE INTENTIONALLY LEFT BLANK



                                       8
<Page>




         IN WITNESS WHEREOF, the parties hereto have executed this Agreement as
of the date first above written.

                                   HAWAIIAN AIRLINES, INC.

                                         /s/ Paul J. Casey
                                       ----------------------------------------
                                       Name: Paul J. Casey
                                       Title: Vice Chairman and Chief Executive
                                              Officer

                                         /s/ Christine R. Deister
                                       ----------------------------------------
                                       Name: Christine R. Deister
                                       Title: Executive Vice President and Chief
                                              Financial Officer


                                   ALOHA SECURITIES & INVESTMENT
                                   COMPANY, a Hawaii Limited Partnership, by its
                                   General Partner:

                                   ALOHA INVESTMENT COMPANY INC., a
                                   Hawaii corporation



                                       /s/ Han H. Ching
                                       ----------------------------------------
                                       Name: Han H. Ching
                                       Title: Vice President



                                   SHERIDAN ING PARTNERS HAWAII, a
                                   Hawaii Limited Partnership, by its General
                                   Partner:

                                   Louise K.Y. Ing and Richard K.M. Ing,
                                   Co-Trustees  of the FLP Trust dated
                                   May 21, 1987


                                   /s/ Louise K.Y. Ing
                                   --------------------------------------------
                                   Name: Lousise K.Y. Ing
                                   Title: Co-Trustee



                                   /s/ RICHARD K.M. ING
                                   --------------------------------------------
                                   Name: Richard K.M. Ing
                                   Title: Co-Trustee


<Page>



                                   SCHEDULE A
                                   ----------

                                 LIST OF SELLERS

<Table>
<Caption>
Seller                                                       No. of Shares
------                                                       -------------
<S>                                                          <C>
Aloha Securities & Investment Company                        3,750
Sheridan Ing Partners Hawaii                                 1,250
                                                             -----
                                                             5,000
</Table>