Born on 19 January 1949 in Coalisland, Northern Ireland, Taylor was the son of a lorry driver, and had six siblings. As an amateur, he won the 1968 British Junior Billiards Championship. Taylor turned professional in 1972. That season he made his debut in the World Snooker Championship at the 1973 event, losing 8–9 to Cliff Thorburn in the first round. Over the next few years, Taylor reached the semi-finals at the event in 1975 where he lost 12–19 to Eddie Charlton, and 1977, losing to Thorburn 18–16. Two years later he reached the 1979 final, but lost 16–24 to qualifier Terry Griffiths. He reached his highest world ranking for the following season, second behind Steve Davis.