Born inInnsbruck, Baur started his career withTirol Innsbruck and played 12 seasons for them, winning four league titles and a domestic cup. In 1997, he went for a short break to Japan and also played a season in the GermanBundesliga forHamburger SV. At 34 years of age, he signed forSV Pasching, and after another four seasons there he decided to make another move and switched toLASK Linz.
Baur made his debut for theAustria national team in a May 1990 friendly match againstthe Netherlands as a substitute forKurt Russ and was a non-playing squad member at the1990 FIFA World Cup. His last international match was an October 2002 European Championship qualifying match, also against the Netherlands. He earned a total of 40 caps, scoring five goals.[2]
Baur was announced as the new head coach ofSV Grödig on 7 May 2014,[3] four days before the final match of the end of the 2013–14 season.[4] He begins in the 2014–15 season.[3] He had been the head coach of the reserve team ofRed Bull Salzburg from the summer of 2012[5] to end of November 2013.[3] He was sacked on 4 June 2015.[6]