Born Harry Grew Crosby on June 4, 1898 in Boston's exclusive "Back Bay" area, he was the son of one of the richest banking families in New England and the nephew of J.P. Morgan, the financier. As such, he was heir to a substantial family fortune.
After serving in the American Field Service Ambulance Corps in World War I, in 1921 Crosby married Mary Phelps Jacob, who took the name Caresse Crosby. Two days after their wedding, they moved to Paris, France, where he worked in his uncle's bank. Drawn to the bohemian lifestyle of the artists gathering in Montparnasse, and desirous of being a poet, Crosby quit his job at his uncle's bank and in April of 1927 he and wife Caresse founded a book publishing company. Originally named Éditions Narcisse, it was later changed to the Black Sun Press. By 1928, Harry Crosby gained some recognition as a poet after the publishing of his Red Skeletons collection said to be heavily indebted to Charles Baudelaire and Edgar Allan Poe.
The Black Sun Press went on to perform important services to the literary community, publishing fiction by D. H. Lawrence and poetry by Archibald MacLeish as well as works by James Joyce, Kay Boyle, and Hart Crane. It also issued two more volumes of Crosby's poetry, Chariot of the Sun and Transit of Venus, which owed as much to Gertrude Stein as his prior poems did to Baudelaire. In 1929, Crosby published his most interesting volume of verse, Mad Queen, displaying the influence of Surrealism.
In the United States, on December 10, 1929, Crosby and Josephine Bigelow, née Rotch, a newly married woman with whom Crosby had been carrying on an affair, committed what was apparently a dual suicide. Crosby's death scandalised the society of the American financial establishment.
Following her husband's death, Caresse Crosby edited his papers and continued the work of the Black Sun Press. She published some of the works of Ernest Hemingway, William Faulkner, Dorothy Parker and others.