The MiG-21 Lancer was flown by Lieutenant-commander Florin Rotaru, 36
According Reuters, eyewitnesses at the airshow, attended by about 4,000 people, said the plane exploded when it hit the ground. The footage shows flames and thick smoke.
Television reports quoted witnesses as saying the pilot might have tried to avoid hitting the crowds and instead chose to crash on a nearby field.
The defense ministry said the cause of the crash, some 240 kilometers (150 miles) east of Bucharest, was being investigated.
It named the dead pilot as Lieutenant-commander Florin Rotaru, 36.
Photo credit: Adelin Petrisor