One of seven children, Moore was born into a farm family in Dozier, Alabama. As a scholarship player from 1958–1962, Moore played as a career backup quarterback for legendary coach Bear Bryant. During his college career at Alabama, Moore earned his bachelor's degree in sociology in 1963 and his master's degree in secondary education in 1964. After he earned his master's degree, at Coach Bryant's suggestion, he joined the Alabama Air National Guard.