EXHIBIT 32(b)

CERTIFICATION PURSUANT TO
18 U.S.C. SECTION 1350

In connection with the Annual Report of Campbell Soup Company (the “Company”) on Form 10-K for the fiscal year ended August 1, 2010 (the “Report”), I, B. Craig Owens, Senior Vice President — Chief Financial Officer and Chief Administrative Officer of the Company, hereby certify, pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, that, to my knowledge:

(1) The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Date: September 29, 2010

By:  /s/  B. Craig Owens

Name:     B. Craig Owens

Title:  Senior Vice President —
Chief Financial Officer and
Chief Administrative Officer