Great Yarmouth-born Hollis made 107 appearances for Norwich as a centre-forward between 1948 and 1952, scoring 59 times. Hollis scored a hat-trick in less than 30 minutes on debut for Norwich. Of all Norwich"s top-20 scorers (see List of Norwich City Football Club club records), his rate of a goal every 1.81 games is the best.
His best return was five goals versus Walsall F.C. in 1951.
After he left Norwich, he played for Tottenham Hotspur F.C. and Southend United F.C. He scored a hat-trick for the latter at Carrow Road in 1954, the "only player to score three times for and against City on the ground."
He was selected to play for the Third Division South representative team in 1956/57and 1957/58.