Frank Earl Klepper was born in Plano, Texas and raised in McKinney, Texas. Klepper studied art at the Art Institute of Chicago in 1914. He worked his way through his training there by having jobs in the Institute cafeteria and worked as an usher in a theatre.
Frank Klepper moved to Dallas in 1927 and was the chairman of the Dallas Woman's Forum where many important exhibits were displayed. He was a successful teacher and best known for his landscapes. He was co-founder of the Southwestern School of Fine Arts. In 1929 he taught in the Dallas Public Schools and in 1930 founded the Klepper Sketch Club.
He was commissioned to paint murals by the Federal Arts Project of the WPA with murals in Prairie View College, Hempstead, Texas and in McKinney, Texas.
Klepper had memberships in the American Artists Professional League; American Federation of Arts; Dallas Woman's Forum; Dallas Art Association; Southern States Art League; and Texas Fine Arts Association and others. He exhibited often, including works in the Annual Texas Artists Exhibition, Fort Worth; Annual Exhibition of Texas Artists, Galveston Cotton Carnival Annual Exhibition; Dallas Woman's Forum and Southern States Art League and others.