Born in Vejle, Jacob Laursen spent his childhood years playing for Vejle Kammeraterne and Vejle Boldklub. He made his senior debut for VB in July 1989, and was named 1989 Danish under-19 Player of the Year. He played at VB until the club was relegated to the secondary Danish 1st Division league in the summer 1992. Laursen represented Denmark at the 1992 Summer Olympics, where he played full-time in Denmark's three matches, before elimination. After the Olympics, Laursen moved to Silkeborg IF, and he went on to captain the Danish under-21 national team. Laursen won the 1994 Danish Superliga championship with Silkeborg IF, and made his Danish national team debut in January 1995. He was selected for the 1995 King Fahd Cup by Danish national team manager Richard Møller Nielsen, and went on to play in every game of the tournament, which Denmark won. He also played a single game for the Danish national team at the 1996 European Championship. In July 1996, Laursen moved abroad to play for English club Derby County in a transfer deal worth £500,000. He spent four seasons at Derby, where he played more than 100 games for the club. He was a part of the Danish national team at the 1998 FIFA World Cup, but wasunimpressive in his single match participation at the tournament. In March 2000, he decided to end his national team career under national team manager Bo Johansson. Laursen cited personal reasons, as well as the booing he received by Danish spectators when he came on as a substitute for his 25th national team game in November 1999. While he did not win over the Danish public, Laursen was selected as team captain for Derby in a number of games, and was named Player of the Year in the 1998–99 season. In the summer 2000, Laursen moved back to Denmark to be closer to his children. He signed a contract with F.C. Copenhagen, moving to the club on a free transfer. In his first year at FCK, the club won the 2001 Superliga championship under manager Roy Hodgson. Before the new season, Laursen criticized FCK for a lack of professionalism, and he left the club in January 2002. He moved back to England to play for Leicester City, in a £400,000 transfer deal. He played ten games for Leicester before his relationship with the club turned sour. After two months at Leicester, he spent a month on loan with the English club Wolverhampton, before being loaned out to Aarhus GF in Denmark for the remainder of the 2001–02 season. He was loaned out to Greek club PAOK Salonika for the entire 2002–03 season, but eventually refused to play for the club. In November 2002, Laursen was given a free transfer by Leicester, which was struggling financially, and he left the club. He signed a contract with Austrian team Rapid Wien, but he was dropped from the team in April 2003. He moved back to Denmark to play on an amateur basis in September 2003, and enlisted at childhood club Vejle Boldklub in the Danish 1st Division. Laursen signed a contract with division rivals FC Fredericia in July 2004, and played with the club until he ended his career in September 2005.
