AT HOME CORP
424B3, 2000-07-17
COMPUTER PROGRAMMING, DATA PROCESSING, ETC.
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<PAGE>   1

PROSPECTUS SUPPLEMENT #6                        FILED PURSUANT TO RULE 424(B)(3)
(TO PROSPECTUS DATED JUNE 7, 2000)                    REGISTRATION NO. 333-32228

                               [EXCITE@HOME LOGO]
                              AT HOME CORPORATION

                         $500,000,000 PRINCIPAL AMOUNT
                 4 3/4% CONVERTIBLE SUBORDINATED NOTES DUE 2006

                        SHARES OF SERIES A COMMON STOCK
                     ISSUABLE UPON CONVERSION OF THE NOTES

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

This prospectus supplement relates to the resale by the holders of 4 3/4%
Convertible Subordinated Notes due 2006 of Excite@Home and the shares of Series
A common stock of Excite@Home issuable upon the conversion of the notes.

You should read this prospectus supplement in conjunction with the prospectus
dated June 7, 2000, which is to be delivered with this prospectus supplement.
All capitalized terms used but not defined in this prospectus supplement shall
have the meanings given to them in the prospectus.

The information in the table appearing under the heading "Selling
Securityholders" in the prospectus is superseded in part by the information
appearing in the table below:

<TABLE>
<CAPTION>
                                PRINCIPAL AMOUNT OF
                                NOTES BENEFICIALLY     PERCENTAGE     SHARES OF SERIES A    SHARES OF SERIES A
                                    OWNED THAT          OF NOTES         COMMON STOCK          COMMON STOCK
             NAME                   MAY BE SOLD        OUTSTANDING    BENEFICIALLY OWNED     THAT MAY BE SOLD
             ----               -------------------    -----------    ------------------    ------------------
<S>                             <C>                    <C>            <C>                   <C>
Salomon Smith Barney Inc. ....      $2,920,000              *               51,666                51,666
</TABLE>

-------------------------
* Less than 1%

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

INVESTING IN OUR CONVERTIBLE SUBORDINATED NOTES OR OUR SERIES A COMMON STOCK
INVOLVES A HIGH DEGREE OF RISK. PLEASE CAREFULLY CONSIDER THE "RISK FACTORS"
BEGINNING ON PAGE 2 OF THE PROSPECTUS.

NEITHER THE SECURITIES AND EXCHANGE COMMISSION NOR ANY STATE SECURITIES
COMMISSION HAS APPROVED OR DISAPPROVED OF THESE SECURITIES OR PASSED UPON THE
ADEQUACY OR ACCURACY OF THIS PROSPECTUS OR THIS PROSPECTUS SUPPLEMENT. ANY
REPRESENTATION TO THE CONTRARY IS A CRIMINAL OFFENSE.

            The date of this prospectus supplement is July 17, 2000.


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