The airport, located at 6500 Mainla Road, was notified of the crash around 2:30 p.m.
The pilot was killed while preparing to practice takeoffs and landings Wednesday afternoon.
The pilot, whose name wasn't immediately released, had been cleared to touch down on a runway and immediately take off again. The pilot then requested permission to make a full-stop landing.
An airport official says the pilot was cleared for a full-stop landing just before the plane crashed about a mile north of the airport.
The Federal Aviation Administration says the plane was a replica of an RAF SE5a, a World War I-era British warplane.
(KUSA-TV © 2012 Multimedia Holdings Corporation with The Associated Press)