Born in New York City on November 14, 1937, Grossman grew up in Mississippi and Georgia during his early life.[1] His teenage years were spent in Pennsylvania where he attended schools in Harrisburg and Philadelphia.[1] He began his professional career as a jazz pianist while a high school student in Philadelphia in the mid 1950s.[4][1] During the latter half of the 1950s he was an active part of the post-bop jazz scene in that city, playing with musicians like trumpeter Lee Morgan; double bassists Jimmy Garrison, Henry Grimes, and Reggie Workman; and saxophonist Odean Pope to name a few.[4][1]
In 1963 Grossman began playing free jazz and he led the New Music Quintet, a Philadelphia free jazz ensemble, in 1965-1965.[1] He produced the first formal Philadelphia concert of free jazz in May 1965.[4] From 1972-1978 he led the rock band Duck Soup, first in Philadelphia and then in San Francisco, California.[1]
In 1978 Grossman moved to Los Angeles and was thereafter primarily active as a solo artist.[1] He did, however, still occasionally lead small groups of musicians with whom he made a few recordings, including In the Air (1989, Nine Winds 0146) and Trio in Real Time (1989–90, Nine Winds 0134).[1] From 1989 until his death in Los Angeles on October 2, 1992 he taught improvised music and jazz on the faculty of the Southern California Institute of Architecture.[1]