Griffin was born and raised in West Baltimore, Maryland, where he lived on Mount Holly Street. He attended Garrison Junior High School and Forest Park High School. He, like his brother Donald Griffin, (who later replaced Marv Tarplin in the Miracles), is a guitarist,as well as a singer, and sang with a local Baltimore group called The Last Dynasty. Damon Harris, who later went on to fame as a member of The Temptations, was a high school friend and group member in another local group, the Tempos. Griffin idolized Miracles lead singer Smokey Robinson, while Harris idolized Temptation Eddie Kendricks. Both of them wound up as replacements for their idols in their respective groups.
Griffin and three friends formed the group Last Dynasty and won a talent program on NBC Television. "It was like a pre-American Idol thing. My group won. We sang `Friendship Train' by Gladys Knight and the Pips," Griffin said. The Last Dynasty won a record deal from RCA as first prize, but never took it. The next week, Griffin was in Detroit, auditioning for Berry Gordy and the Motown executives. He was the 60th guy they brought in to audition to replace Smokey Robinson - and Griffin got the job.
During The Miracles' nationwide 1972 Farewell Tour with Smokey Robinson, Griffin was introduced by Robinson as his replacement in The Miracles as lead singer. After a year of woodshedding with Motown's famous Artist Development Dept., Griffin released his first single with The Miracles, "What Is A Heart Good For", from their first post-Robinson album, Renaissance in 1973. Griffin sang this song on his first national television appearance as a Miracle with the remaining group members of The Miracles, Bobby Rogers, Ronnie White, and Pete Moore on another NBC music program, The Midnight Special, in 1973, hosted by Robinson. The single was withdrawn and replaced with a ballad, "Don't Let It End (Till You Let It Begin)", which was a mild hit. After a second single, "Give Me Just Another Day", was released later that year, The Miracles released "Do It Baby" in 1974, which peaked at #4 on the Billboard R&B charts and became the group's first bona-fide hit with Griffin.
Like Robinson before him, Griffin co-wrote many of the Miracles' songs, in addition to singing lead. Griffin and original Miracles member Pete Moore wrote all of the Miracles' 1975 platinumselling album, City of Angels. During his tenure with the group, they recorded three hits: "Do It Baby" in 1974, and the Miracles' most successful single, the number-one hit "Love Machine", in 1975 which sold 4.5 million records worldwide. Griffin also sung lead on "Don't Cha Love It", a Top 10 R&B #4 single.