Kennedy then spent the next six years pursuing a graduate degree in English at the University of Michigan but did not complete his Ph.D.
His first book, Nude Descending a Staircase, won the 1961 Lamont Poetry Prize of the Academy of American Poets, and his dozens of books have won awards, including Guggenheim and National Arts Council fellowships, a grant from the National Endowment for the Arts, the Bess Hokin Prize from Poetry magazine, and a Los Angeles Times Book Award for poetry (in 1985 for Cross Ties: Selected Poems), the 1969–1970 Shelley Memorial Award, the Golden Rose of the New England Poetry Club, honorary degrees from Lawrence and Adelphi Universities and Westfield State College.
Kennedy received the National Council of Teachers of English Year 2000 Award for Excellence in Children's Poetry.
[4] Kennedy also wrote a series of children's poetry books (Brats), translated Aristophanes' Lysistrata into English, and edited the anthology Tygers of Wrath: Poems of Hate, Anger, and Invective (University of Georgia Press, 1981).
With his wife Dorothy and scholar Jane E. Aaron, he is the editor of The Bedford Reader, a collegiate literature textbook used for teaching to the AP English Language and Composition test.