Strupar played in Belgium for KRC Genk, winning promotion to the Belgian First Division in 1996 and becoming champion of Belgium with the same team in 1999. He also won the Belgian Golden Shoe as Player of the Year for 1998. In 1998, he finished as top scorer with 22 goals. He moved to Derby County in December 1999, where he most notably scored the first British league goal of the year 2000 after two minutes against Watford. While at Derby Strupar gained popularity with his prolific scoring ability.
Despite an excellent goals-to-games ratio when fit, injuries curtailed his Derby career, and he was eventually given a free transfer, with which he returned to Croatia for a brief spell at Dinamo Zagreb to wind up his career.
Strupar currently lives in Zagreb with his wife, daughters Dora and Laura and his son Bruno, born 16 March 2007. He is also currently a sport commentator on the Croatian network RTL for Premier League broadcasts along with Filip Brkić.