Throughout his playing career, Curran represented several clubs, including Ards F.C., Finn Harps F.C., Derry City F.C., and Dundalk F.C.
During the 1986–87 League of Ireland First Division season, Curran made 26 appearances for Finn Harps.
Later, he served as the captain of Derry City F.C., where he participated in the team's treble-winning 1988–1989 season.
[3] Curran holds the record for the second-highest number of appearances for Derry City ever, a total of 512.
His last appearance for the club came on 29 October 2002 at Windsor Park during a County Antrim Shield match.