He was born in West Memphis in 1927 or 1932.
He first came to blues as a harmonica player, and backed Howlin' Wolf when he came to West Memphis in 1948.
By 1950, parker, now known as "Little Junior" due to the closeness with Wolf, had formed a band with pianist Bill Johnson. Known as Little Junior's Blue Flames, the band included Matt Murphy and L.C. Dranes and they were recorded by Ike Turner for Modern Records early in 1952.
Parker was now solely a vocalist.
The following year Pat Hare and John Bowers replaced Murphy and Dranes on guitar and drums respectively, and the band began to record for Sam Phillips' new Sun label. Their first record, "Feelin' Good" was a hit, so much so that Parker was soon signed by Duke/Peacock in Houston in 1954. Johnson took over the Blue Flames and together they made several hits such as "Mother In Law Blues" and Barefoot Rock".
Parker later recorded in a soul style and he only occasionally reverted to blues with harp.
He died in Chicago 1971.