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Hibbett began his studies of Japanese as a sophomore at Harvard College 1942 before working as a language specialist for the US Army in 1942-46. After graduating from Harvard College in 1947, he went on to receive his Ph.D., also from Harvard, in 1950. He taught at UCLA before returning to Harvard as a professor in 1958. He was Director of the Edwin O. Reischauer Institute of Japanese Studies from 1985 through 1988.
His publications include studies and translations of Edo and modern literature. He is particularly known for his translations of Tanizaki and works on Japanese language teaching. On March 16, 2018, he was awarded the Lindsley and Masao Miyoshi Translation Prize "for lifetime achievement as a translator of Edo period and modern Japanese literature" by the Donald Keene Center of Japanese Culture at Columbia University, New York.
- Floating World in Japanese Fiction, Oxford University Press, New York 1959
- Modern Japanese; a Basic Reader, Harvard University Press, Cambridge (Mass.) 1965
- Contemporary Japanese Literature: an Anthology of Fiction, Film, and Other Writing since 1945, Alfred A. Knopf, New York 1977
- The Chrystanthemum and the Fish: Japanese Humor Since the Age of the Shoguns, Kodansha International, Tōkyō New York 2002
- The Key by Jun'ichirō Tanizaki, Alfred A. Knopf, New York 1961
- Seven Japanese Tales by Jun'ichirō Tanizaki, Alfred A. Knopf, New York 1963
- Diary of a Mad Old Man by Jun'ichirō Tanizaki, Alfred A. Knopf, New York 1965 Review
- Harp of Burma by Michio Takeyama, Charles E. Tuttle Co., Rutland (Vt.) 1966
- Beauty and sadness by Yasunari Kawabata, Alfred A. Knopf, New York 1975
- Quicksand by Jun'ichirō Tanizaki, Alfred A. Knopf, New York 1994 Review
- A portrait of Shunkin by Jun'ichirō Tanizaki, Limited Editions Club, New York 2000