Born Arlette B. Broil in New Orleans, Louisiana, she was steeped in church music as a child. She sang for a while with the Southern Harps, had her own radio show in New Orleans, and later appeared in night clubs, on Broadway and in 1962 on both The Ed Sullivan Show and The Dinah Shore Show.
Griffin performed briefly with "Queen of Gospel" Albertina Walker and The Caravans in 1953-1954 but spent most of her career as a solo artist. While often compared to Mahalia Jackson, Griffin had a lighter contralto that allowed her to achieve more vocal pyrotechnics — holding a note for long periods of time, continuing a song for as long as twenty minutes and ranging through three octaves.
Griffin began her known recording career with the Gospel Consolators, an a cappella group in New Orleans, in the late 1940s. They issued several 78 rpm shellac records with her billed as lead vocalist.
After moving to Chicago in 1951, she worked briefly with The Caravans, a gospel group led by Albertina Walker, making a session with them for States in 1954. She left the group later that year, recording as a soloist for Al Benson's Parrot label. After moving to Los Angeles she was signed in 1956 by Art Rupe of Specialty Records. After collaboration with Robert "Bumps" Blackwell, she recorded an album on the Decca label with an orchestra: "It Takes a Lot of Love"; she made "Portraits in Bronze" on Liberty; and joined the lucrative night club circuit singing and recording gospel albums in night clubs in the 1960s. She recorded a solo album for Savoy which was unremarkable except as a great example of her voice, and an album with the Gospel Pearls entitled "Gospel Soul" on Sunset, a subsidiary of Liberty. The Nashboro label released an album recorded live in concert in stereo and Griffin continued to tour and record as her health allowed, up to her death. There is an album on the Spirit Feel label which samples her four-decade long recording career.
In 1974 she appeared in the 20th Century Fox thriller, Together Brothers, which was filmed in Galveston, Texas. She played a female preacher, "Reverend Brown", who conducts a funeral service for a murdered policeman. The only witness to the crime is a little boy who is stalked and his "brothers" pull together and help apprehend the killer. The soundtrack for the movie was scored by Barry White.
Griffin was sampled in the 1996 dance track "I Know The Lord" by the band The Tabernacle. The same sample was also used in 1999 for the Shaboom track "Bessie".