<PAGE>   1

                                                                   Exhibit 10.37

THE SECURITIES REPRESENTED HEREBY HAVE BEEN ACQUIRED PURSUANT TO REGULATION S OF
THE SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"), AND MAY NOT BE SOLD,
MORTGAGED, PLEDGED, HYPOTHECATED OR OTHERWISE TRANSFERRED EXCEPT IN ACCORDANCE
THEREWITH, PURSUANT TO A REGISTRATION UNDER THE ACT OR PURSUANT TO AN AVAILABLE
EXEMPTION FROM REGISTRATION. THE ISSUER OF THESE SECURITIES MAY REQUIRE AN
OPINION OF COUNSEL IN FORM AND SUBSTANCE SATISFACTORY TO THE ISSUER TO THE
EFFECT THAT ANY PROPOSED TRANSFER OR RESALE IS IN COMPLIANCE WITH THE ACT AND
ANY APPLICABLE STATE SECURITIES LAWS. IN ADDITION, NO HEDGING TRANSACTION MAY BE
CONDUCTED WITH RESPECT TO THESE SECURITIES UNLESS SUCH TRANSACTIONS ARE IN
COMPLIANCE WITH THE ACT.

THE SECURITIES REPRESENTED HEREBY AND THE SECURITIES TO BE ISSUED UPON ITS
EXERCISE HAVE NOT BEEN REGISTERED UNDER THE ACT AND MAY NOT BE EXERCISED BY OR
ON BEHALF OF ANY `U.S. PERSON' (AS DEFINED IN REGULATION S UNDER THE ACT) UNLESS
REGISTERED UNDER THE ACT OR AN EXEMPTION FROM SUCH REGISTRATION IS AVAILABLE.



                                  AVIGEN, INC.

WARRANT FOR THE PURCHASE OF SHARES OF COMMON STOCK



No. ________                                                     ________ Shares



        FOR VALUE RECEIVED, AVIGEN, INC., a Delaware corporation (the
"Company"), with its principal office at 1201 Harbor Bay Parkway, #1000,
Alameda, California 94502, hereby certifies that __________ ("Holder"), or its
assigns, is entitled, subject to the provisions of this Warrant, to purchase
from the Company, at any time before 5:00 p.m. (Pacific Time) on the expiration
date of [five years from closing date]; provided, however, that the expiration
date shall be extended by one day for each day since the issuance of this
Warrant on which there has been effective a Suspension Period, as that term is
defined in the Common Stock and Warrant Purchase Agreement dated February 16,
1999, pursuant to which this Warrant was issued (the "Expiration Date"), the
number of fully paid and nonassessable shares of Common Stock of the Company set
forth above, subject to adjustment as hereinafter provided.

        Holder may purchase such number of shares of Common Stock at a purchase
price per share (as appropriately adjusted pursuant to Section 6 hereof) of
_____ Dollars and _____ Cents ($____) (the "Exercise Price"). The term "Common
Stock" shall mean the aforementioned Common Stock of the Company, together with
any other equity securities that may be issued by the Company in addition
thereto or in substitution therefor as provided herein.

        SECTION 1.    EXERCISE OF WARRANT.


                                       1.
<PAGE>   2


                (a) This Warrant may be exercised in whole or in part on any
business day prior to the Expiration Date by presentation and surrender hereof
to the Company at its principal office at the address set forth in the initial
paragraph hereof (or at such other address as the Company may hereafter notify
Holder in writing) with the Purchase Form annexed hereto duly executed and
accompanied by proper payment of the Exercise Price in lawful money of the
United States of America in the form of a check, subject to collection, for the
number of Warrant Shares specified in the Purchase Form. If this Warrant should
be exercised in part only, the Company shall, upon surrender of this Warrant,
execute and deliver a new Warrant evidencing the rights of Holder thereof to
purchase the balance of the Warrant Shares purchasable hereunder. Upon receipt
by the Company of this Warrant and such Purchase Form, together with proper
payment of the Exercise Price, at such office, Holder shall be deemed to be the
holder of record of the Warrant Shares, notwithstanding that the stock transfer
books of the Company shall then be closed or that certificates representing such
Warrant Shares shall not then be actually delivered to Holder. The Company shall
pay any and all documentary stamp or similar issue or transfer taxes payable in
respect of the issue or delivery of the Warrant Shares.

        SECTION 2. RESERVATION OF SHARES. The Company hereby agrees that at all
times there shall be reserved for issuance and delivery upon exercise of this
Warrant all shares of its Common Stock or other shares of capital stock of the
Company from time to time issuable upon exercise of this Warrant. All such
shares shall be duly authorized and, when issued upon such exercise in
accordance with the terms of this Warrant, shall be validly issued, fully paid
and nonassessable, free and clear of all liens, security interests, charges and
other encumbrances or restrictions on sale (other than as provided in the
Company's certificate of incorporation and any restrictions on sale set forth
herein or pursuant to applicable federal and state securities laws) and free and
clear of all preemptive rights.

        SECTION 3. FRACTIONAL INTEREST. The Company will not issue a fractional
share of Common Stock upon exercise of a Warrant. Instead, the Company will
deliver its check for the current market value of the fractional share. The
current market value of a fraction of a share is determined as follows: multiply
the current market price of a full share by the fraction of a share and round
the result to the nearest cent.

        The current market price of a share of Common Stock for purposes of this
Section only is the Quoted Price (as defined in Section 6(b) below) of the
Common Stock on the last trading day prior to the exercise date.

        SECTION 4.    ASSIGNMENT OR LOSS OF WARRANT.

               (a) Except as provided in Section 9, Holder shall be entitled,
without obtaining the consent of the Company, to assign its interest in this
Warrant in whole or in part to any person or persons. Subject to the provisions
of Section 9, upon surrender of this Warrant to the Company or at the office of
its stock transfer agent or warrant agent, with the Assignment Form annexed
hereto duly executed and funds sufficient to pay any transfer tax, the Company
shall, without charge, execute and deliver a new Warrant or Warrants in the name
of the assignee or assignees named in such instrument of assignment (any such
assignee will then be a "Holder" for purposes of this Warrant) and, if Holder's
entire interest is not being assigned, in the name of Holder, and this Warrant
shall promptly be canceled.


<PAGE>   3


                (b) Upon receipt of evidence satisfactory to the Company of the
loss, theft, destruction or mutilation of this Warrant, and (in the case of
loss, theft or destruction) of indemnification satisfactory to the Company, and
upon surrender and cancellation of this Warrant, if mutilated, the Company shall
execute and deliver a new Warrant of like tenor and date.

        SECTION 5. RIGHTS OF HOLDER. Holder shall not, by virtue hereof, be
entitled to any rights of a stockholder in the Company, either at law or equity,
and the rights of Holder are limited to those expressed in this Warrant. Nothing
contained in this Warrant shall be construed as conferring upon Holder hereof
the right to vote or to consent or to receive notice as a stockholder of the
Company on any matters or with respect to any rights whatsoever as a stockholder
of the Company. No dividends or interest shall be payable or accrued in respect
of this Warrant or the interest represented hereby or the Warrant Shares
purchasable hereunder until, and only to the extent that, this Warrant shall
have been exercised in accordance with its terms.

        SECTION 6. ADJUSTMENT OF EXERCISE PRICE AND NUMBER OF SHARES. The number
and kind of securities purchasable upon the exercise of this Warrant and the
Exercise Price shall be subject to adjustment from time to time upon the
beginning of certain events, as follows:

                (a) Adjustment for Change in Capital Stock. If at any time after
the date hereof the Company:

                        (A) pays a dividend or makes a distribution on its
Common Stock in shares of its Common Stock;

                        (B) subdivides its outstanding shares of Common Stock
into a greater number of shares;

                        (C) combines its outstanding shares of Common Stock into
a smaller number of shares;

                        (D) makes a distribution on its Common Stock in shares
of its capital stock other than Common Stock; or

                        (E) issues by reclassification of its Common Stock any
shares of its capital stock;

then the number and kind of securities purchasable upon the exercise of this
Warrant and the Exercise Price in effect immediately prior to such action shall
be adjusted so that Holder may receive upon exercise of this Warrant and payment
of the same aggregate consideration the number of shares of capital stock of the
Company which Holder would have owned immediately following such action if
Holder had exercised this Warrant immediately prior to such action.

        The adjustment shall become effective immediately after the record date
in the case of a dividend or distribution and immediately after the effective
date in the case of a subdivision, combination or reclassification.


<PAGE>   4


               (b) Current Market Price. The "current market price" per share of
Common Stock on any date is the average of the Quoted Prices of the Common Stock
for the 30 consecutive trading days commencing 45 trading days before the date
in question. The "Quoted Price" of the Common Stock is the last reported sales
price of the Common Stock as reported by the Nasdaq National Market, or the
primary national securities exchange on which the Common Stock is then quoted;
provided, however, that if the Common Stock is neither traded on the Nasdaq
National Market nor on a national securities exchange, the price referred to
above shall be the price reflected on the Nasdaq National Market, or if the
Common Stock is not then traded on the Nasdaq National Market, the price
reflected in the over-the counter market as reported by the National Quotation
Bureau, Inc. or any organization performing a similar function.

               (c) Minimum Adjustment. No adjustment in the Exercise Price of
this Section 6 shall be required unless such adjustment would require an
increase or decrease of at least twenty-five cents ($.25) in such Exercise
Price; provided, however, that any adjustments which by reason of this
subsection are not required to be made, shall be carried forward and taken into
account in any subsequent adjustment. All calculations under this Section 6
shall be made to the nearest cent or to the nearest share, as the case may be.

               (d) Deferral of Issuance or Payment. In any case in which an
event covered by this Section 6 shall require that an adjustment in the Exercise
Price be made effective as of a record date, the Company may elect to defer
until the occurrence of such event (i) issuing to Holder, if this Warrant is
exercised after such record date, the shares of Common Stock and other capital
stock of the Company, if any, issuable upon such exercise over and above the
shares of Common Stock or other capital stock of the Company, if any, issuable
upon such exercise on the basis of the Exercise Price in effect prior to such
adjustment, and (ii) paying to Holder by check any amount in lieu of the
issuance of fractional shares pursuant to Section 3.

               (e) When No Adjustment Required. No adjustment need be made for a
change in the par value of the Common Stock. To the extent this Warrant becomes
exercisable into cash, no adjustment need be made thereafter as to the cash, and
interest will not accrue on the cash.

               (f) Notice of Certain Actions. In the event that:

                        (A) the Company shall authorize the issuance to all
holders of its Common Stock of rights, warrants, options or convertible
securities to subscribe for or purchase shares of its Common Stock or of any
other subscription rights, warrants, options or convertible securities; or

                        (B) the Company shall authorize the distribution to all
holders of its Common Stock of evidences of its indebtedness or assets (other
than dividends paid in or distributions of the Company's capital stock for which
the Exercise Price shall have been adjusted pursuant to subsection (a) of this
Section 6 or cash dividends or cash distributions payable out of consolidated
current or retained earnings as shown on the books of the Company and paid in
the ordinary course of business); or

                        (C) the Company shall authorize any capital
reorganization or reclassification of the Common Stock (other than a subdivision
or combination of the


<PAGE>   5


outstanding Common Stock and other than a change in par value of the Common
Stock) or of any consolidation or merger to which the Company is a party and for
which approval of any stockholders of the Company is required (other than a
consolidation or merger in which the Company is the continuing corporation and
that does not result in any reclassification or change of the Common Stock
outstanding), or of the conveyance or transfer of the properties and assets of
the Company as an entirety or substantially as an entirety; or

                        (D) the Company is the subject of a voluntary or
involuntary dissolution, liquidation or winding-up procedure; or

                        (E) the Company proposes to take any action that would
require an adjustment of the Exercise Price pursuant to this Section 6;

then the Company shall cause to be mailed by first-class mail to Holder, at
least twenty (20) days prior to the applicable record or effective date
hereinafter specified, a notice stating (x) the date as of which the holders of
Common Stock of record to be entitled to receive any such rights, warrants or
distributions are to be determined, or (y) the date on which any such
consolidation, merger, conveyance, transfer, dissolution, liquidation or
winding-up is expected to become effective, and the date as of which it is
expected that holders of Common Stock of record shall be entitled to exchange
their shares of Common Stock for securities or other property, if any,
deliverable upon such reorganization, reclassification, consolidation, merger,
conveyance, transfer, dissolution, liquidation or winding-up.

        SECTION 7. OFFICERS' CERTIFICATE. Whenever the Exercise Price shall be
adjusted as required by the provisions of Section 6, the Company shall forthwith
file in the custody of its Secretary or an Assistant Secretary at its principal
office an officers' certificate showing the adjusted Exercise Price determined
as herein provided, setting forth in reasonable detail the facts requiring such
adjustment and the manner of computing such adjustment. Each such officers'
certificate shall be signed by the chairperson, president or chief financial
officer of the Company and by the secretary or any assistant secretary of the
Company. Each such officers' certificate shall be made available at all
reasonable times for inspection by Holder.

SECTION 8. RECLASSIFICATION, REORGANIZATION, CONSOLIDATION OR MERGER. In the
event of any reclassification, capital reorganization or other change of
outstanding shares of Common Stock of the Company (other than a subdivision or
combination of the outstanding Common Stock and other than a change in the par
value of the Common Stock) or in the event of any consolidation or merger of the
Company with or into another corporation (other than a merger in which the
Company is the continuing corporation and that does not result in any
reclassification, capital reorganization or other change of outstanding shares
of Common Stock of the class issuable upon exercise of this Warrant) or in the
event of any sale, lease, transfer or conveyance to another corporation of the
property and assets of the Company as an entirety or substantially as an
entirety, the Company shall, as a condition precedent to such transaction, cause
effective provisions to be made so that Holder shall have the right thereafter,
by exercising this Warrant, to purchase the kind and amount of shares of stock
and other securities and property (including cash) receivable upon such
reclassification, capital reorganization and other change, consolidation,
merger, sale or conveyance by a holder of the number of shares of Common Stock
that might have been received upon exercise of this Warrant


<PAGE>   6


immediately prior to such reclassification, capital reorganization, change,
consolidation, merger, sale or conveyance. Any such provision shall include
provisions for adjustments in respect of such shares of stock and other
securities and property that shall be as nearly equivalent as may be practicable
to the adjustments provided for in this Warrant. The foregoing provisions of
this Section 8 shall similarly apply to successive reclassifications, capital
reorganizations and changes of shares of Common Stock and to successive
consolidations, mergers, sales or conveyances. In the event that in connection
with any such capital reorganization, or reclassification, consolidation,
merger, sale or conveyance, additional shares of Common Stock shall be issued in
exchange, conversion, substitution or payment, in whole or in part, for, or of,
a security of the Company other than Common Stock, any such issue shall be
treated as an issue of Common Stock covered by the provisions of subsection (a)
of Section 6.

        SECTION 9. TRANSFER TO COMPLY WITH THE SECURITIES ACT OF 1933. This
Warrant may not be exercised and neither this Warrant nor any of the Warrant
Shares, nor any interest in either, may be offered, sold, assigned, pledged,
hypothecated, encumbered or in any other manner transferred or disposed of, in
whole or in part, except in compliance with applicable United States federal and
state securities or Blue Sky laws, including Regulation S under the Act, and the
terms and conditions hereof. Each Warrant shall bear the legends in
substantially the same form as the legends set forth on the first page of this
Warrant. Each certificate for Warrant Shares issued upon exercise of this
Warrant, unless at the time of exercise such Warrant Shares are acquired
pursuant to a registration statement that has been declared effective under the
Act, and applicable blue sky laws shall bear a legend substantially in the
following form:

        THE SECURITIES REPRESENTED HEREBY HAVE BEEN ACQUIRED PURSUANT TO
        REGULATION S OF THE SECURITIES ACT OF 1933, AS AMENDED (THE
        "ACT"), AND MAY NOT BE SOLD, MORTGAGED, PLEDGED, HYPOTHECATED OR
        OTHERWISE TRANSFERRED EXCEPT IN ACCORDANCE THEREWITH, PURSUANT
        TO A REGISTRATION UNDER THE ACT OR PURSUANT TO AN AVAILABLE
        EXEMPTION FROM REGISTRATION. THE ISSUER OF THESE SECURITIES MAY
        REQUIRE AN OPINION OF COUNSEL IN FORM AND SUBSTANCE SATISFACTORY
        TO THE ISSUER TO THE EFFECT THAT ANY PROPOSED TRANSFER OR RESALE
        IS IN COMPLIANCE WITH THE ACT AND ANY APPLICABLE STATE
        SECURITIES LAWS. IN ADDITION, NO HEDGING TRANSACTION MAY BE
        CONDUCTED WITH RESPECT TO THESE SECURITIES UNLESS SUCH
        TRANSACTIONS ARE IN COMPLIANCE WITH THE ACT.

Any certificate for any Warrant Shares issued at any time in exchange or
substitution for any certificate for any Warrant Shares bearing such legend
(except a new certificate for any Warrant Shares issued after the acquisition of
such Warrant Shares pursuant to a registration statement that has been declared
effective under the Act) shall also bear such legend unless, in the opinion of
counsel for the Company, the Warrant Shares represented thereby need no longer
be subject to the restriction contained herein. The provision of this Section 9
shall be binding upon all subsequent holders of certificates for Warrant Shares
bearing the above legend and all subsequent holders of this Warrant, if any.


<PAGE>   7


        SECTION 10. MODIFICATION AND WAIVER. Neither this Warrant nor any term
hereof may be changed, waived, discharged or terminated other than by an
instrument in writing signed by the Company and by Holder.

        SECTION 11. NOTICES. Any notice, request or other document required or
permitted to be given or delivered to Holder or the Company shall be delivered
or shall be sent by certified mail, postage prepaid, to Holder at its address as
shown on the books of the Company or to the Company at the address indicated
therefor in the first paragraph of this Warrant.

        SECTION 12. DESCRIPTIVE HEADINGS AND GOVERNING LAW. The description
headings of the several sections and paragraphs of this Warrant are inserted for
convenience only and do not constitute a part of this Warrant. This Warrant
shall be construed and enforced in accordance with, and the rights of the
parties shall be governed by, the laws of the State of California, without
regard to its conflicts of laws principles.



<PAGE>   8


        IN WITNESS WHEREOF, the Company has duly caused this Warrant to be
signed by its duly authorized officer and to be dated as of [_________ ___],
1999.





                                        AVIGEN, INC.



                                        By:
                                           -------------------------------------
                                           John Monahan, Ph.D.
                                           President and Chief Executive Officer




                                       8.
<PAGE>   9


                                  PURCHASE FORM

                                                       Dated ___________, 19____





        The undersigned hereby irrevocably elects to exercise the within Warrant
No. _________ to purchase _________ shares of Common Stock and hereby makes
payment of $_____________ in payment of the exercise price thereof. In addition,
the undersigned represents that it is not a U.S. Person within the meaning
specified in Regulation S under the Securities Act of 1933, as amended, that it
is not exercising the Warrant on behalf of a U.S. Person, and that it is
exercising the Warrant outside of the United States.







                                            HOLDER



                                            By:
                                               ---------------------------------

                                            Print Name:
                                                       -------------------------

                                            Title:
                                                  ------------------------------




                                       9.
<PAGE>   10


                                 ASSIGNMENT FORM

                                                         Dated _________, 19____



        FOR VALUE RECEIVED, ________________ hereby sells, assigns and transfers
unto __________________________________________________ (the "Assignee"),
         (please type or print in block letters)
________________________________________________________________________________
                             (insert address)
its right to purchase up to _______ shares of Common Stock represented by this
Warrant No. _________ and does hereby irrevocably constitute and appoint
____________________________ attorney, to transfer the same on the books of the
Company, with full power of substitution in the premises.

                                            HOLDER



                                            By:
                                               ---------------------------------

                                            Print Name:
                                                       -------------------------



                                       10