The 200 police cadets were traveling to Kabul from neighboring Wardak province, where they were in training, for leave for the Muslim holiday of Eid, in five buses when the convoy was attacked.
Paghman District Chief Haji Musa Khan told CBS News there was an initial explosion which appeared to be smaller, but prompted the buses to stop as the cadets tended to the wounded. There was then a larger second blast.
"More than 30 people were killed and nearly 100 others wounded" Musa Khan said, "the bomber detonated his vehicle in between two buses."
It was not immediately confirmed that the second and larger of the two explosions was the suicide car bomb, or whether the first explosion could also have been caused by a suicide bomber.
Musa Khan added that the death toll could rise.
According to the Associated Press, the attack occurred just 13 miles from Kabul, and the Taliban claimed responsibility in a statement.
Ministry of Interior spokesperson Sediq Seddiqi said the ministry was working to confirm the details of the "terrorist attacks on a police convey in Kabul."