The aircraft, operated by the Indonesian Aero Sport Federation, went down in Ciampea area at around 10.00 am local time, shortly after taking off from Atang Sendjaja Airport in Bogor at 9.08 am, Xinhua reported.
The plane was piloted by former Indonesian Air Force spokesman Fajar Adriyanto, with civilian Roni Ahmad serving as co-pilot.
Adriyanto died in the crash, while Ahmad sustained serious injuries. Both were taken to a nearby hospital.
Indonesian Air Force spokesman I Nyoman Suadnyana confirmed the aircraft was in airworthy condition before departure.
Authorities are investigating the cause of the accident.