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                                                                    EXHIBIT 10.3


THIS WARRANT AND THE UNDERLYING SECURITIES HAVE NOT BEEN REGISTERED UNDER THE
SECURITIES ACT OF 1933, AS AMENDED (THE "ACT"). THEY MAY NOT BE SOLD, OFFERING
FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF AN EFFECTIVE REGISTRATION
STATEMENT AS TO SUCH SECURITIES UNDER THE ACT OR AN OPINION OF COUNSEL
SATISFACTORY TO THE CORPORATION THAT SUCH REGISTRATION IS NOT REQUIRED.


                                 WEBSENSE, INC.

                        WARRANT TO PURCHASE COMMON STOCK


NO. CW-2                                                          APRIL 15, 1999


                            VOID AFTER APRIL 15, 2002

     THIS CERTIFIES THAT, for value received, Alps System Integration Co., Ltd.,
with its principal office at 1-7 Yukigaya - Otsuka - Cho, Ota - Ku, Tokyo,
145-0067 Japan, or assigns (the "Holder"), is entitled to subscribe for and
purchase at the Exercise Price (defined below) from WebSENSE, INC., a Delaware
corporation, with its principal office at 10240 Sorrento Valley Road, San Diego,
California (the "Corporation") up to fifty thousand (50,000) shares of the
Common Stock of the Corporation (the "Common Stock").

     1. DEFINITIONS. As used herein, the following terms shall have the
following respective meanings:

          (a) "Exercise Period" shall mean the period commencing with the date
hereof and ending three years from the date hereof, unless sooner terminated as
provided below.

          (b) "Exercise Price" shall mean $0.05 per share, subject to adjustment
pursuant to Section 5 below.

          (c) "Exercise Shares" shall mean the shares of the Corporation's
Common Stock upon exercise of this Warrant.

     2. EXERCISE OF WARRANT. The rights represented by this Warrant may be
exercised in whole or in part at any time during the Exercise Period, by
delivery of the following to the Corporation at its address set forth above (or
at such other address as it may designate by notice in writing to the Holder):

          (a) An executed Notice of Exercise in the form attached hereto;

          (b) Payment of the Exercise Price either (i) in cash or by check, or
(ii) by cancellation of indebtedness; and

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          (c) This Warrant.

     Upon the exercise of the rights represented by this Warrant, a certificate
or certificates for the Exercise Shares so purchased, registered in the name of
the Holder or persons affiliated with the Holder, if the Holder so designates,
shall be issued and delivered to the Holder within a reasonable time after the
rights represented by this Warrant shall have been so exercised.

     The person in whose name any certificate or certificates for Exercise
Shares are to be issued upon exercise of this Warrant shall be deemed to have
become the holder of record of such shares on the date on which this Warrant was
surrendered and payment of the Exercise Price was made, irrespective of the date
of delivery of such certificate or certificates, except that, if the date of
such surrender and payment is a date when the stock transfer books of the
Corporation are closed, such person shall be deemed to have become the holder of
such shares at the close of business on the next succeeding date on which the
stock transfer books are open.

     2.1 NET EXERCISE. Notwithstanding any provisions herein to the contrary, if
the fair market value of one share of the Corporation's Common Stock is greater
than the Exercise Price (at the date of calculation as set forth below), in lieu
of exercising this Warrant by payment of cash, the Holder may elect to receive
shares equal to the value (as determined below) of this Warrant (or the portion
thereof being canceled) by surrender of this Warrant at the principal office of
the Company together with the properly served endorsed Notice of Exercise in
which event the Company shall issue to the Holder a number of shares of Common
Stock computed using the following formula.

     X  = Y (A-B)
          -------
             A

Where        X =    the number of shares of Common Stock to be issued to Holder

             Y =    the number of shares of Common Stock purchasable under
                    the Warrant or, if only a portion of the Warrant is being
                    exercised, the portion of the Warrant being canceled (at
                    the date of such calculation)

             A =    the fair market value of one share of the Corporation's
                    Common Stock (at the date of such calculation)

             B =    Exercise Price (as adjusted to the date of such calculation)

     For purposes of the above calculation, the fair market value of one share
of Common Stock shall be determined by the Company's Board of Directors in good
faith; provided, however, that in the event that this Warrant is exercised
pursuant to this Section 2.1 in connection with the Company's initial public
offering of its Common Stock, the fair market value per share shall be the per
share offering price to the public of the Company's initial public offering.

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     3. COVENANTS OF THE CORPORATION.

     3.1 COVENANTS AS TO EXERCISE SHARES. The Corporation covenants and agrees
that all Exercise Shares that may be issued upon the exercise of the rights
represented by this Warrant will, upon issuance, be validly issued and
outstanding, fully paid and nonassessable, and free from all taxes, liens and
charges with respect to the issuance thereof. The Corporation further covenants
and agrees that the Corporation will at all times during the Exercise Period,
have authorized and reserved, free from preemptive rights, a sufficient number
of shares of its Common Stock to provide for the exercise of rights represented
by this Warrant. If at any time during the Exercise Period the number of
authorized but unissued shares of Common Stock shall not be sufficient to permit
exercise of this Warrant, the Corporation will take such corporate action as
may, in the opinion of counsel, be necessary to increase its authorized but
unissued shares of Common Stock to such number of shares as shall be sufficient
for such purposes.

     3.2 NO IMPAIRMENT. Except and the extent as waived or consented to by the
Holder, the Corporation will not, by amendment of its Certificate of
Incorporation or through any reorganization, transfer of assets, consolidation,
merger, dissolution, issue or sale of securities or any other voluntary action,
avoid or seek to avoid the observance or performance of any of the terms to be
observed or performed hereunder by the Corporation, but will at all times in
good faith assist in the carrying out of all the provisions of this Warrant and
in the taking of all such action as may be necessary or appropriate in order to
protect the exercise rights of the Holder against impairment.

     3.3 NOTICES OF RECORD DATE. In the event of any taking by the Corporation
of a record of the holders of any class of securities for the purpose of
determining the holders thereof who are entitled to receive any dividend (other
than a cash dividend which is the same as cash dividends paid in previous
quarters) or other distribution, the Corporation shall mail to the Holder, at
least ten (10) days prior to the date specified herein, a notice specifying the
date on which any such record is to be taken for the purpose of such dividend or
distribution.

     4. REPRESENTATIONS OF HOLDER.

     4.1 ACQUISITION OF WARRANT FOR PERSONAL ACCOUNT. The Holder represents and
warrants that it is acquiring the Warrant solely for its account for investment
and not with a view to or for sale or distribution of said Warrant or any part
thereof. The Holder also represents that the entire legal and beneficial
interests of the Warrant and Exercise Shares the Holder is acquiring is being
acquired for, and will be held for, its account only.

     4.2  SECURITIES ARE NOT REGISTERED.

          (a) The Holder understands that the Warrant and the Exercise Shares
     have not been registered under the Securities Act of 1933, as amended (the
     "Act") on the basis that no distribution or public offering of the stock of
     the Corporation is to be effected. The Holder realizes that the basis for
     the exemption may not be present if, notwithstanding its representations,
     the Holder has a present intention of acquiring the securities for a fixed
     or determinable period in the future, selling (in connection with a
     distribution or

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     otherwise), granting any participation in, or otherwise distributing the
     securities. The Holder has no such present intention.

          (b) The Holder recognizes that the Warrant and the Exercise Shares
     must be held indefinitely unless they are subsequently registered under the
     Act or an exemption from such registration is available. The Holder
     recognizes that the Corporation has no obligation to register the Warrant
     or the Exercise Shares of the Corporation, or to comply with any exemption
     from such registration.

          (c) The Holder is aware that neither the Warrant nor the Exercise
     Shares may be sold pursuant to Rule 144 adopted under the Act unless
     certain conditions are met, including, among other things, the existence of
     a public market for the shares, the availability of certain current public
     information about the Company, the resale following the required holding
     period under Rule 144 and the number of shares being sold during any three
     month period not exceeding specified limitations. Holder is aware that the
     conditions for resale set forth in Rule 144 have not been satisfied and
     that the Corporation presently has no plans to satisfy these conditions in
     the foreseeable future.

     4.3  DISPOSITION OF WARRANT AND EXERCISE SHARES.

          (a)  The Holder further agrees not to make any disposition of all or
     any part of the Warrant or Exercise Shares in any event unless and until:

               (i) The Corporation shall have received a letter secured by the
          Holder from the Securities and Exchange Commission stating that no
          action will be recommended to Commission with respect to the proposed
          disposition; or

               (ii) There is then in effect a registration statement under the
          Act covering such proposed disposition and such disposition is made in
          accordance with said registration statement; or

               (iii) The Holder shall have notified the Corporation of the
          proposed disposition and shall have furnished the Corporation with a
          detailed statement of the circumstances surrounding the proposed
          disposition, and if reasonably requested by the Company, the Holder
          shall have furnished the Corporation with an opinion of counsel,
          reasonably satisfactory to the Company, for the Holder to the effect
          that such disposition will not require registration of such Warrant or
          Exercise Shares under the Act or any applicable state securities laws.

          (b) The Holder understands and agrees that all certificates evidencing
     the shares to be issued to the Holder may bear the following legend:

               THESE SECURITIES HAVE NOT BEEN REGISTERED UNDER THE SECURITIES
               ACT OF 1933, AS AMENDED (THE "ACT"). THEY MAY NOT BE SOLD,
               OFFERED FOR SALE, PLEDGED OR HYPOTHECATED IN THE ABSENCE OF AN
               EFFECTIVE REGISTRATION STATEMENT AS TO THE SECURITIES UNDER THE
               ACT OR AN OPINION OF

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               COUNSEL SATISFACTORY TO THE COMPANY THAT SUCH REGISTRATION IS NOT
               REQUIRED.

          (c) The Holder hereby agrees not to sell or otherwise transfer or
     dispose of all or any part of this Warrant or the Exercise Shares during a
     period specified by the representative of the underwriters of Common Stock
     (not to exceed one hundred eighty (180) days) following the effective date
     of the registration statement of the Corporation filed under the Act.
     Holder further agrees that the Corporation may impose stop-transfer
     instructions with respect to securities subject to the foregoing
     restrictions until the end of such period.

     5. ADJUSTMENT OF EXERCISE PRICE. In the event of changes in the outstanding
Common Stock of the Corporation by reason of stock dividends, split-ups,
recapitalizations, reclassifications, combinations or exchanges of shares,
separations, reorganizations, liquidations, or the like, the number and class of
shares available under the Warrant in the aggregate and the Exercise Price shall
be correspondingly adjusted to give the Holder of the Warrant, on exercise for
the same aggregate Exercise Price, the total number, class, and kind of shares
as the Holder would have owned had the Warrant been exercised prior to the event
and had the Holder continued to hold such shares until after the event requiring
adjustment; provided, however, that such adjustment shall not be made with
respect to, and this Warrant shall terminate if not exercised prior to, the
events set forth in Section 7 below. The form of this Warrant need not be
changed because of any adjustment in the number of Exercise Shares subject to
this Warrant.

     6. FRACTIONAL SHARES. No fractional shares shall be issued upon the
exercise of this Warrant as a consequence of any adjustment pursuant hereto. All
Exercise Shares (including fractions) issuable upon exercise of this Warrant may
be aggregated for purposes of determining whether the exercise would result in
the issuance of any fractional share. If, after aggregation, the exercise would
result in the issuance of a fractional share, the Corporation shall, in lieu of
issuance of any fractional share, pay the Holder otherwise entitled to such
fraction a sum in cash equal to the product resulting from multiplying the then
current fair market value of an Exercise Share by such fraction.

     7. EARLY TERMINATION. In the event of, at any time during the Exercise
Period, an initial public offering of securities of the Corporation registered
under the Act, or any capital reorganization, or any reclassification of the
capital stock of the Corporation (other than a change in par value or from par
value to no par value or no par value to par value or as a result of a stock
dividend or subdivision, split-up or combination of shares), or the
consolidation or merger of the Corporation with or into another corporation
(other than a merger solely to effect a reincorporation of the Corporation into
another state), or the sale or other disposition of all or substantially all the
properties and assets of the Corporation in its entirety to any other person,
the Corporation shall provide to the Holder twenty (20) days advance written
notice of such public offering, reorganization, reclassification, consolidation,
merger or sale or other disposition of the Corporation's assets, and this
Warrant shall terminate unless exercised prior to the date such public offering
is closed or the occurrence of such reorganization, reclassification,
consolidation, merger or sale or other disposition of the Corporation's assets.

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<PAGE>   6

     8. NO STOCKHOLDER RIGHTS. This Warrant in and of itself shall not entitle
the Holder to any voting rights or other rights as a stockholder of the
Corporation.

     9. TRANSFER OF WARRANT. Subject to applicable laws, the restriction on
transfer set forth on the first page of this Warrant, this Warrant and all
rights hereunder are transferable, by the Holder in person or by duly authorized
attorney, upon delivery of this Warrant and the form of assignment attached
hereto to any transferee designated by Holder. The transferee shall sign an
investment letter in form and substance satisfactory to the Corporation.

     10. LOST, STOLEN, MUTILATED OR DESTROYED WARRANT. If this Warrant is lost,
stolen, mutilated or destroyed, the Corporation may, on such terms as to
indemnify or otherwise as it may reasonably impose (which shall, in the case of
a mutilated Warrant, include the surrender thereof), issue a new Warrant of like
denomination and tenor as the Warrant so lost, stolen, mutilated or destroyed.
Any such new Warrant shall constitute an original contractual obligation of the
Corporation, whether or not the allegedly lost, stolen, mutilated or destroyed
Warrant shall be at any time enforceable by anyone.

     11. NOTICES, ETC. All notices and other communications required or
permitted hereunder shall be in writing and shall be sent by telex, telegram,
express mail or other form of rapid communications, if possible, and if not then
such notice or communication shall be mailed by first-class mail, postage
prepaid, addressed in each case to the party entitled thereto at the following
addresses: (a) if to the Corporation, to WebSENSE, INC., Attention: Chief
Executive Officer, 10240 Sorrento Valley Road, San Diego, CA 92123, and (b) if
to the Holder, to Alps System Integration Co., Ltd., Attention: President, 1-7
Yukigaya -- Otsuka -- Cho, Ota -- Ku, Tokyo, 145-0067, Japan, or at such other
address as one party may furnish to the other in writing. Notice shall be deemed
effective on the date dispatched if by personal delivery, telecopy, telex or
telegram, two days after mailing if by express mail, or three days after mailing
if by first-class mail.

     12. ACCEPTANCE. Receipt of this Warrant by the Holder shall constitute
acceptance of and agreement to all of the terms and conditions contained herein.

     13. GOVERNING LAW. This Warrant and all rights, obligations and liabilities
hereunder shall be governed by the laws of the State of California.

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     IN WITNESS WHEREOF, the Corporation has caused this Warrant to be executed
by its duly authorized officer effective as of April 15, 1999.

                                        WEBSENSE, INC.


                                        By /s/ John B. Carrington
                                           -------------------------------------

                                        Its Chairman & CEO
                                            ------------------------------------


ATTEST:


Carrie Carlander
----------------------------------------
Secretary

<PAGE>   8

                               NOTICE OF EXERCISE

TO: WEBSENSE, INC.

     1. [ ] The undersigned hereby elects to purchase ______ shares of the
Common Stock of WebSENSE, INC. (the "Company") pursuant to the terms of the
attached Warrant, and tenders herewith payment of the exercise price in full,
together with all applicable transfer taxes, if any.

        [ ] The undersigned hereby elects to purchase ______ shares of the
Common Stock of WebSENSE, INC. (the "Company") pursuant to the terms of the net
exercise provisions set forth in Section 2.1 of the attached Warrant, and shall
tender payment of all applicable transfer taxes, if any.

     2. Please issue a certificate or certificates representing said shares of
Common Stock in the name of the undersigned or in such other name as is
specified below:

                           --------------------------
                                     (Name)

                           --------------------------

                           --------------------------
                                    (Address)


     3. The undersigned represents that (i) the aforesaid shares of Common Stock
are being acquired for the account of the undersigned for investment and not
with a view to, or for resale in connection with, the distribution thereof and
that the undersigned has no present intention of distributing or reselling such
shares; (ii) the undersigned is aware of the Company's business affairs and
financial condition and has acquired sufficient information about the Company to
reach an informed and knowledgeable decision regarding its investment in the
Company; (iii) the undersigned is experienced in making investments of this type
and has such knowledge and background in financial and business matters that the
undersigned is capable of evaluating the merits and risks of this investment and
protecting the undersigned's own interest; (iv) the undersigned understands that
the shares of Common Stock issuable upon exercise of this Warrant have not been
registered under the Securities Act of 1933, as amended (the "Securities Act"),
by reason of a specific exemption from the registration provisions of the
Securities Act, which exemption depends upon, among other things, the bona fide
nature of the investment intent as expressed herein, and, because such
securities have not been registered under the Securities Act, they must be held
indefinitely unless subsequently registered under the Securities Act or an
exemption from such registration is available; (v) the undersigned is aware that
the aforesaid shares of Common Stock may not be sold pursuant to Rule 144
adopted under the Securities Act unless certain conditions are met and until the
undersigned has held the shares for the number of years prescribed by Rule 144,
that among the conditions for use of the Rule is the availability of current
information to the public about the Company and the Company has not made such
information available and has no present plans to do so; and (vi) the
undersigned agrees not to make any disposition of all or any part of the
aforesaid shares of Common Stock unless and until there is then in effect a
registration statement under the Securities Act covering

<PAGE>   9

such proposed disposition and such disposition is made in accordance with said
registration statement, or the undersigned has provided the Company with an
opinion of counsel satisfactory to the Company, stating that such registration
is not required.


-------------------------               ----------------------------------------
Date                                    (Signature)


                                        ----------------------------------------
                                        (Print Name)


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                                 ASSIGNMENT FORM

               (To assign the foregoing Warrant, execute this form and
               supply required information. Do not use this form to
               purchase shares.)


     FOR VALUE RECEIVED, the foregoing Warrant and all rights evidenced thereby
are hereby assigned to

Name:
      --------------------------------------------------------------------------
                                 (Please Print)

Address:
         -----------------------------------------------------------------------
                                 (Please Print)

Dated:
       ----------------------

Holder's
Signature:
           -----------------------------

Holder's
Address:
          ------------------------------


NOTE: The signature to this Assignment Form must correspond with the name as it
appears on the face of the Warrant, without alteration or enlargement or any
change whatever. Officers of corporations and those acting in a fiduciary or
other representative capacity should file proper evidence of authority to assign
the foregoing Warrant.