The KAI T-50 Golden Eagle, a US-South Korean-made light attack aircraft, spun out of control on Sunday.
It crashed into an air force base complex near Adi Sutjipto Airport in Yogyakarta, a tourist destination city on the main island of Java, a witness, Jawardi, said. .
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The crash occurred on the second day of the air show that is celebrating the 70th anniversary of the Air Force Flight School in Yogyakarta, Air Vice-Marshal Dwi Badarmanto, an air force spokesman, said.
The pilot and co-pilot - both Indonesians - died instantly, and an investigation team has been sent to the crash site, he said.
An Indonesian Air Force's T-50 Golden Eagle plane crashes during an air show in Yogyakarta on Sunday.
An Indonesian Air Force's T-50 Golden Eagle plane crashes during an air show in Yogyakarta on Sunday. Photo: Supplied
TV showed plumes of black smoke billowing from the wreckage as the plane burst into flames.
The trainer aircraft is one of 16 similar models bought by the Indonesian Air Force last year.