Galloway played defensive end and defensive tackle for Coach Doug Dickey and Coach Charley Pell’s teams from 1978 to 1981. During Galloway's junior season in 1980, he was a member of the Gators team that posted the biggest one-year turnaround in the history of NCAA Division I football from 0–10–1 in 1979 to an 8–4 bowl team in 1980.
Galloway finished with 21 career sacks, good enough for seventh all-time in Gator history and was recognized as a second-team All-SEC selection and an honorable mention All-American in 1980. As a senior team captain in 1981, Galloway was a first-team All-SEC selection, and a Football Writers Association of America first-team All-American. He was later inducted into the University of Florida Athletic Hall of Fame as a "Gator Great."
Galloway was a second round pick (#38 overall) of the St. Louis Cardinals in the NFL in 1982. He played with the Cardinals for eight seasons and his last two with the Denver Broncos.