Kavianpour has played most of his career for Persepolis where he had several good seasons, playing in the midfield with his great skill and dribbling.
During 2001 and 2002 some English clubs showed interest in him and he had trials with clubs such as Bolton Wanderers, Newcastle United FC, and Reading F.C., but Persepolis preferred that he sign a one-year contract with UAE club Al Wasl in July 2002.
In May 2006 he signed a two-year contract to play for Turkish club Kayserispor in Turkish Premier Super League.
On September 22, 2006 the Turkish club announced that they will release the Iranian midfielder as he was allegedly tested positive for doping after the match against Erciyesspor.
The Turkish Football Federation banned Kavianpour from playing in Turkey for 2 years, however Kavianpour planned to appeal to the Turkish Football Federation in order to reduce the ban. The ban was later reduced to 1 year.