The crash is believed to have occurred in front of horrified onlookers.
It comes nine months after a pilot walked away from an emergency crash landing at the airfield, which is used for small aircraft, pilot training and recreational aviation.
An Australian Transport Safety Bureau said it is believed someone was trying to start the aircraft when it taxied away.
There were unconfirmed reports that a dog was removed from one plane after the crash, which occurred in a plane parking area.
Word of the tragedy spread quickly around the airport.
Cadet pilot Alex Garbett, 28, said he could not understand how the incident occurred.
"It's an absolute freak accident," he said.
"You see (minor incidents) happen once every six months but I've never heard of a fatality."
Another pilot, who wished to remain anonymous, was also stunned.
"We have no idea what happened," he said. "Obviously one of them has gotten away."
Flights were not affected by the crash, but some pilots who landed were unable to access hangars while authorities investigated the crash.
In March 2013, a Spitfire replica crashed during the Classic Jets Air Show at Parafield Airport.
Roger Stokes, 73, was killed when the amateur-built scale replica Spitfire he was flying slammed into the ground between two clothes shops and about 200m from a soccer match.
An ATSB report found that Stokes was flying too slowly while executing a left turn to remain airborne and his aircraft was not fitted with an aerodynamic stall warning device.
