Rasmussen scored 37 goals in 60 matches for various Denmark national youth sides and was named the Danish under-19 Player of the Year in 2003.
Born in Copenhagen, Rasmussen lived in Valby until he was two years old, at which point he and his parents moved to Tilst,[1] 10 km west of Aarhus.
Following two goals in 15 games in the first half of the 2002–03 Superliga season, Rasmussen signed an improved five-year contract running until the summer of 2008.
With a price tag of 12 million DKK,[5] he replaced striker Morten Skoubo who had been sold to Spanish club Real Sociedad.
[6] His start at Brøndby was marked by an injury incurred in March 2006, and in the remaining games of the 2005–06 Superliga season, he scored one goal in six matches.
He returned in February 2007, helping Brøndby win the 2007 Royal League cup tournament, and went on to score 15 goals in 13 games in the second half of the 2006–07 Superliga season.
Following 12 goals in 15 games in the first half of the 2009–10 Superliga, Rasmussen attracted the attention of Scottish Premier League club Celtic.
[7] On 25 January 2010, Rasmussen arrived in Glasgow for contract negotiations and a medical with Celtic before signing on a three-and-a-half-year deal the next day for a fee in excess of £1 million.
[15] Rasmussen rarely featured for Celtic under the management of Neil Lennon, making only four starts during his time with the club.
[22] In December, Mainz's sporting director Christian Heidel announced the club would not be making a permanent move after the end of the loan deal.
However, at the main tournament, Rasmussen had to relinquish his place in the starting line-up to Nicklas Bendtner, though he played as a substitute in all three Denmark games.
Rasmussen made his debut for the senior Danish national team on 11 October 2008, as he played the last 13 minutes of the 3–0 win against Malta in the 2010 World Cup qualification.
[35] After retiring at the end of the 2018/19 season, FC Midtjylland announced, that they had hired Duncan as a forward coach.
Other former players such as Kristian Bach Bak, Jens Berthel Askou and Søren Mussmann also played for TIF All Stars.