Grossman was born in New York City in 1927. He served in the U.S. Navy from 1945 to 1946, then attended Haverford College, graduating in 1948 with a Bachelor of Arts degree. He went on to attend Harvard, earning a Master of Arts degree in 1949.

Grossman then returned to New York City, where he lived for the rest of his life. From 1951 to 1961, he edited East Europe magazine, the journal of the National Committee for a Free Europe, an anti-communist Central Intelligence Agency (CIA) front organization.

In 1959, he published his first novel, Acrobat Admits (1959). It was an early example of the wave of black comedy that swept through American fiction in the early 1960s. In the book, a handsome New Yorker seduces two different women, falls for one, and murders a man. "Mine," he told The New York Times reviewer Anthony Boucher, "is that country where the frontier between the possible and the not possible is unmarked." Boucher found the book unsuccessful but "dazzling and delightful." Most reviewers found it slick and amoral, but Marvin Mudrick, in a Hudson Review roundup of a dozen novels, called it "the most perverse and in many ways the most promising of the dozen."

From Wikipedia