An authoritative black character actor of film and TV, Gunn also enjoyed a successful career on stage. He made his New York City stage debut in the original off-Broadway production of Jean Genet's The Blacks (1962). He performed many Shakespearean roles in Joseph Papp's Shakespeare in the Park, winning an Obie Award for his portrayal of Aaron in Titus Andronicus. He won a second Obie for his work in the NEC produced First Breeze of Summer, which moved to Broadway. His acclaimed performance as Othello at the Stratford, Connecticut Shakespeare Festival moved to Broadway in 1970. Other Broadway plays in which Gunn performed are: A Hand is on the Gate, Twelfth Night, I Have a Dream, and The Poison Tree. He was nominated for a Tony Award nomination for Best Actor for The Poison Tree.

Born in St. Louis, Missouri, of African descent the son of Mary and George Gunn, a labourer he was one of seven siblings. After his mother died, his family separated. Moses left home and rode the railroad at just 12 years old. He returned to St. Louis and attended school while living at the home of Jewel Richie, his English Teacher. He graduated from Tennessee State University after serving in the United States Army, then went to graduate school at Kansas University, gaining a master's degree. He taught briefly at Grambling College before attempting an acting career in NYC. He married Gwendolyn Mumma Landes in 1966, becoming stepfather to her daughter Kirsten Sarah Landes. They had a son, Justin Moses, in 1970 who became a musician and Composer in the Copenhagen-based band, "The Reverend Shine Snake Oil Co."

He may be best remembered in film for his portrayal of mobster Ellsworth Raymond "Bumpy" Jonas in the first two Shaft movies, Booker T. Washington in the 1981 movie Ragtime, a performance which won him an NAACP Image Award, and as Cairon, the Childlike Empress' imperial physician, in the 1984 film The NeverEnding Story. He was nominated for an Emmy Award in 1977 for his role in the TV mini-series Roots. He also co-starred with Avery Brooks on the TV series A Man Called Hawk. Gunn appeared in six episodes as atheist shop owner Carl Dixon on Good Times, as boxer-turned-farmer Joe Kagan on Little House on the Prairie, and as "Moses Gage" in Father Murphy. In 1989, Gunn appeared in two episodes of The Cosby Show as two different characters. His final acting role was as murder suspect Risley Tucker in "Three Men and Adena", an episode of Homicide: Life on the Street.

He died from complications of asthma in Guilford, Connecticut on December 16, 1993. He was survived by his wife Gwendolyn, a son, Justin, of Guilford; a daughter, Kirsten Landes Mudd of Philadelphia, as well as a brother and three sisters.