He died Tuesday at North Mississippi Medical Center in Tupelo after a long illness, according to Holland-Harris Funeral Directors.
Simmons — not to be confused with the Kiss bassist with the same name — was in show business for more than 50 years, working with such names as Sam Phillips and the Bill Black Combo. More recently, he co-wrote "Indian Outlaw," which became a big hit in 1994 for country superstar Tim McGraw.
But his biggest success came in 1964 with the novelty song "Haunted House," which reached No. 11 on the Billboard pop chart and launched Simmons on a world tour.
Among other early gigs, he performed as an opening act for Presley in Tupelo, Presley's birthplace and Simmons' longtime hometown, as Presley's career was taking off, said his son, Cary Simmons.
After appearing in some Memphis clubs, Simmons signed with Sun Records, the legendary Memphis label formed by Phillips that launched the careers of Presley, Johnny Cash and other stars.
While he didn't have the chart success of other Sun performers, Simmons' recordings have become known to later generations through reissues. Brian Setzer did a version of Simmons' "Peroxide Blonde in a Hopped Up Model Ford" on his "Rockabilly Riot Vol. 1: A Tribute to Sun Records."
Simmons, born in Itawamba County in 1937, spent most of his life in Northeast Mississippi although he lived for a time in Memphis. Besides his son, survivors include his mother, a sister, and two brothers.