Venc began his career in mountain racing, in which he raced from 1988 to 1994. In 1991 he competed in the Czech Ford Fiesta Cup and finished fourth in the overall standings. In 1991 and 1992 he started in the DTM at his home race in Brno, in 1993 he competed in the DTM for the entire season and finished 20th with one point. In 1994 he switched to the Peugeot 306 Cup and finished fourth. In 1995 he started in the German Super Touring Car Cup and was 22nd in the overall standings, he also drove in the Czech Touring Car Championship and was seventh in the overall standings. In 1996 he remained loyal to this series and became a master. In 1997 and 1998 he drove in the Central European Touring Car Championship and was champion in each case. In 1999 he drove in the Czech Ford Puma Cup. In 2000 he was involved in endurance racing. From 2001 to 2005 he competed in isolated races of the FIA GT in the NGT or GT2 class.