His biggest hit was "You Can't Be True, Dear" (1948), which was first released as an instrumental, and later that year re-released with a vocal by Jerry Wayne dubbed in.
It was in the 1940s in Aurora, Illinois, that Griffin broke into the nightclub circuit, playing at the Rivoli Cafe nightly.
The sessions at the Rivoli were broadcast on the radio station, WMRO, and the program became popular.
Griffin died on March 11, 1956, in Chicago, Illinois, at the age of 46, of a heart attack, and was buried at Lincoln Memorial Park in Aurora.
His version of "Ebb Tide" was played in the fifth-season premiere of the TV drama Mad Men.