The accident happened at the Hirt airfield, near the town of Friesach in the southern province of Carinthia.
The pilot, a 50-year-old local man, made a steep ascent and then went into a quick descent before crashing, Friesach police chief Marianne Makoru told the Austria Press Agency.
The air show was halted after the crash. About 500 spectators attended on Sunday, but Makoru said that "no other people were in danger.
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