Curran began riding for his local cycling club Stockton Wheelers and at the age of 14 completed a ten-mile time trial at Crathorne, North Yorkshire in 24–49. It was obvious he had talent when in 1977 he dominated the English schools national grass and track championship winning all three individual titles in the over-15-years category. Curran earned his first international selection for Great Britain in the San SebastianEuropa Cup match. Although he rose to prominence in time trails and track events, he soon established himself as one of Britain's top road racers. In 1982 he rode for England in the Girvan pro/am three-day and was the highest placed British amateur on overall classification finishing 5th the race was won by Tony Doyle. However his season was still primarily based around track events. Impressive results, winning several national track events led to selection for England, at the 1982 Commonwealth Games in Brisbane, Queensland, Australia. He competed on the track in the 10-mile scratch event and team pursuit. He won his first commonwealth medal taking the bronze medal in the team pursuit. Curran continued to perform well on the track and competed at the World Championships in 1983 in the team pursuit and 50 km point's race. In 1984 he showed his versatility winning the Girvan three-day overall classification was well as the King of the Mountains and sprint competition. Later that season he competed in the 1984 Olympic Games in the team pursuit and points race. In 1985 Curran began focusing more on road racing, retaining his title in the Girvan three-day and was 4th overall in the Milk Race. He was also 3rd in the British Road Race Championship behind Jeff Williams and Paul Watson. After winning the Premier Calendar series and he competed in his first World road race championships in which he finished 29th. In 1986 Curran was offered the chance to turn professional with Raleigh – Weinmann, however he decided to turn it down preferring to stay amateur. In 1986 he won two gold medals on the road at the Commonwealth Games in Edinburgh, Scotland, one in the team time trial and one in the road race. In 1987 he won the Amateur National Road Race Championship. That season he also won his third record breaking Premier Calendar series title in a row. In 1988 Curran was selected for the Olympic Games road race finishing 36th, the race was won by Olaf Ludwig. After dominating the British amateur scene for several years in 1989 Curran finally turned professional. He joined Percy Bilton riding alongside Bob Downs and Steve Joughin. In his first season, he won the British National professional Criterium championships and was 6th in the Kellogg's Tour of Britain, finishing ahead of Sean Kelly. However, when in 1990 the British-based professional season collapsed, Curran was left without a team and he reverted to amateur status in 1991. He went down with double pneumonia and subsequently missed half of the season but bounced back in 1992 finishing 3rd in the British Road Race Championship. He competed in motor-paced racing towards the end of his career including the last ever motor-paced World Championships in Sicily in 1994, His career ended when he broke his back in a serious accident during the Tour of the Pennines in 1996.
Retirement
Paul became occupied with his son, Karl in 1997 giving him a new hobby. Curran owns Paul Curran Cycle Sport in Stockton. A time-served turner and ex-ICI apprentice on Teesside, he also builds wheels for Planet X.