Having already accepted God's call to preach at the age of seventeen, he continued his education at Benedict College, Columbia, South Carolina, earning a Bachelor of Arts degree in 1953.
He led the membership to build two new sanctuaries and a family life center that became the model for many other churches in the Greenville area.
Cureton, then vice president-at-large, took over the leadership of the convention when his predecessor Henry Lyons was forced to resign.
He was an advocate on state issues such as the establishment of a holiday honoring Martin Luther King Jr. in Greenville County.
Cureton was out front in integrating the public libraries in Greenville County, South Carolina.