Floyd Griffin was born and raised in Milledgeville, Georgia. Griffin holds an associate's degree in funeral service from Grupton Jones College, a bachelor's in building construction from Tuskegee Institute, and a master's degree in contract procurement and management from the Florida Institute of Technology. He is also a graduate of the Army Command and General Staff College and the National War College. Griffin is the first African American mayor of Milledgeville.

Floyd Griffin is vice president of Slater Funeral Home in Milledgeville, a Griffin family-owned business. He served 23 years in the U.S. military beginning in 1967. Griffin was a helicopter pilot and flight instructor in Vietnam, then served a tour in Germany, where he was a logistics officer, battalion chief, and director of engineering and housing. He was later assigned to the Pentagon. Following his retirement from the military in 1990, Griffin taught military science at Wake Forest University and Winston-Salem State University.

Floyd Griffin is currently the Mayor of Milledgeville, Georgia. He was elected to this position in 2001, and has served 6 terms in this position. His first political position was as a Georgia State Senator, and he was elected in 1994. Since then, he has run for Lieutenant Governor of Georgia in 1998, State Senate in 2010, State House of Representatives in 2016, and Georgia Secretary of State in 2022 but lost all of these races.