Dvořák made his international debut at junior competitions of the FIS in 2003. At the Junior World Championships in 2003, however, he only achieved placements beyond the top thirty. A year later at the Junior World Championships in Stryn he managed to reach the top 30, but a success remained. From March 2004 he started in the B-World Cup of Nordic Combined. In Rovaniemi he was able to win the bronze medal together with the team at the Junior World Championship in 2005. A year later in Kranj he won bronze in the sprint. On March 12, 2006 he made his debut in the Nordic Combined World Cup in Oslo . At the Nordic World Ski Championships 2007 in Sapporo Dvořák reached 7th place with the team in the team competition. In the sprint he reached 24th place, in Gundersen 25th. In the 2007/08 World Cup season , he won World Cup points for the first time and thus reached 41st place in the overall Sprint World Cup ranking. In the World Cup season 2008/09 he achieved his best result so far with 31st place in the overall World Cup. At the 2010 Olympic Winter Games in Vancouver he was 39th in the individual on the normal hill and 28th in the individual on the large hill. In the team competition he reached 8th place together with Aleš Vodseďálek , Tomáš Slavík and Pavel Churavý .
Czech Republic
Oberwiesenthal
Bischofshofen
2010 Vancouver
2014 Sochi
2018 Pyeongchang