Feed, when used with a preposition, is most often used with on:

Tom seeks to escape from regularity by romanti­cism. He feeds on detective and adventure stories — James T. Farrell, The League of Frightened Philis­tines, 1945

When writing turns to mush, thought, which feeds on writing, suffers from malnutrition —Thomas H. Middleton, Saturday Rev., 24 Nov. 1979

Feed has also been used with upon or off. Although still less frequent than on, recent evidence suggests that the use of upon and off has been growing:

... to think again; to feed upon memory —Walter De la Mare, Encounter, December 1954

... shifted his stance toward his art and the experi­ence that his art fed upon —Donald Davie, N.Y. Times Book Rev., 25 Apr. 1976

The dread of the new place mounts up in her and feeds off the complaints in his letters —Oscar Han-dlin, The Uprooted, 1951

... have the sort of hardcover sale that... the soft-cover could feed off the celebrity —N. R. KJeinfield, N.Y. Times Book Rev., 16 Sept. 1979

Feed may even occur with from, but this seems to be a far from usual combination:

... in a position to reward those who ... are content to feed from officially provided sources —Thomas B. Littlewood, Saturday Rev., 15 Apr. 1972

(资料出处：韦伯斯特英语用法词典)