Daughter Patrice Dillon says her father died Wednesday at her home of lung and prostate cancer.
She says Dillon had been diagnosed with cancer in June and underwent surgery to remove a brain tumor earlier this year.
Leonard Dillon began his career using the stage name Jack Sparrow in the early 1960s. He recorded a series of ska songs, including Bull Whip, which featured a young Bob Marley on backing vocals.
Dillon later formed The Ethiopians, a trio whose best known hits were Train to Skaville and Everything Crash.
Dillon is survived by seven children.