Born in Fort Smith, Arkansas, Gunn was in the United States Navy from 1945 to 1946.
He received an Artium Baccalaureus degree from Westminster College in 1950 and a Juris Doctor from Washington University School of Law in 1955.
After leaving the navy, he worked in private practice in St. Louis, Missouri from 1955 to 1971.
In 1982, then-Governor Kit Bond appointed Gunn to the Missouri Supreme Court, where he sat until 1985.
[2] Among the cases over which Gunn presided was a lawsuit against Dillard's Department Stores alleging religious bias, and resulting in a settlement approved by Gunn that prohibited Dillards from requiring employees to work the sabbath.