This church is named for Rev. Melvin E .Peavy, who was pastor of First Church, Cordele, when he died suddenly. Four years later, in this new subdivision of Cordele, with the help of the congregation of First, the Peavy Memorial Church was organized on September 12, 1958. Fred Maddox, a student at Candler School of Theology and a probationary member of the conference, was assigned as pastor. There were been 64 members at the organizational meeting in the cafeteria of Blackshear Trail School. By March 12, 1961, the first unit was completed and Rev. Theo Gee was assigned as pastor. in 1984 they had a sanctuary, educational unit and fellowship hall.
In 1959, the church sponsored a Boy Scout Troop and, in 1960, purchased a parsonage. In 1965, the UMM was organized.