Peters was born in Springfield, Missouri, to Frank Lewis Peters, Sr. and Mary Frissel. He graduated from Drury College in 1951 with a bachelor of arts degree in English. He spent the next two years in the Army (1951–1953), before attending graduate school at Iowa State University. Frank returned to his hometown in 1954 to serve the local radio stations KWTO (AM) and KGBX-FM as news writer and editor. He left Springfield for the Arkansas Gazette in 1957, and returned for the second time to join the Springfield Leader & Press in 1959. In 1962, Peters was named the managing editor of the Rome Daily American. After two years, Peters left Italy to work for the St. Louis Post Dispatch. He was named the publication's music critic in 1967 and became the arts editor in 1984, holding the position until his retirement in 1988. Peters died of a heart attack at St. Anthony's Medical Center in St. Louis on September 17, 2007. He was 76.
Peters was married to Alba Manciani, with whom he had two children.
- Fischer, Heinz Dietrich; Fischer, Erika J. (2002). Complete Biographical Encyclopedia of Pulitzer Prize Winners, 1917–2000. Walter de Gruyter. p. 186. ISBN 9783598301865.
- Brennan, Elizabeth A.; Clarage, Elizabeth C. (1999). Who's who of Pulitzer Prize Winners. Greenwood Publishing Group. p. 92. ISBN 9781573561112.
- Fischer, Heinz Dietrich (1992). Cultural Criticism, 1969–1990. Walter de Gruyter. p. 37. ISBN 9783598301766.
- "Frank Peters Jr. Won Pulitzer Prize as Post-Dispatch music critic". St. Louis Post Dispatch. September 16, 2007.