Career
He has played 43 matches and scored 15 goals for various Danish youth national teams, most recently the Danish national under-21 team Curth signed his first youth contract with Danish club Farum BK when he turned 16. He was called up for various Danish youth national teams, debuting for the under-16 squad in March 2000.
After several training sessions with Dutch club Feyenoord Rotterdam, he was brought into the youth setup of the club in April 2001.
He had a hard time forcing his way into the Feyenoord line-up. He was loaned out to Dutch team Excelsior Rotterdam for the 2004-2005 season, where he made his senior debut and scored eight goals in 19 games.
When his contract with Feyenoord expired in July 2005, he returned to Denmark to play for Aalborg Boldspilklub (AaB) in the Danish Superliga championship. On 10. June 2014, Curth signed with Viborg FF on a free transfer.