The aircraft was a single engine, single wing replica World War I aircraft which was involved in a practice display at the time.
The pilot, a 68-year-old man from Horsham, was the only person onboard. He was pronounced dead at the scene.
The investigation is being led by the Air Accident Investigation Branch with support from Hampshire Constabulary.
Anyone who saw the crash or the plane flying immediately beforehand is asked to contact Hampshire Constabulary on 101.