Kürner won the giant slalom of the Whistler Cup in 2000 and drove his first FIS race in December 2002. From 2004 to 2007 he took part in four Junior World Championships . He achieved his best results in 2007 in Altenmarkt / Flachau : He was among the top ten in all four individual races and thus won the bronze medal in the combination calculated from the times of slalom, giant slalom and downhill. From 2005 to 2007 he won five Slovenian junior championship titles. In the European Cup , Kürner has been regularly at the start since the 2006/2007 season. On November 9th, 2007 he finished sixth in the indoor slalom in the ski hall in Landgraaf for the first time among the top ten. During the next four years this was his best European Cup result. He achieved another top 10 result only once during this time, on March 13, 2009 with ninth place in the giant slalom in Crans-Montana . In March 2010 he became Slovenian champion in giant slalom.
In the World Cup , Kürner has been in action since November 2008 in the disciplines of slalom, giant slalom and the rare super combination. In his 16th World Cup race, the Super Combined by Bansko on February 27, 2011, he won his first and so far only World Cup points as 19th. In the slalom and giant slalom disciplines, he has not yet been able to qualify for the second round of the fastest 30. On December 21, 2011, Kürner achieved his first podium in the European Cup with second place in the City Event in St. Vigil / Kronplatz . 13 months later, on January 27, 2013, he celebrated his first European Cup victory in the slalom on the Großer Arber .