Bedfordshire Police have confirmed the pilot, who was in his 40s but has not been officially named, was pronounced dead shortly after the incident.
The accident happened at around 9.45am at Old Warden Aerodrome, home to the Shuttleworth Collection, where hundreds of people were attending a Military Pageant Air Show.
Members of Bedfordshire Police, with Bedfordshire and Luton Fire and Rescue Service, East of England Ambulance Service and the aerodrome’s fire service, attended to assist the pilot.
The incident is being investigated by the Air Accident Investigation Branch (AAIB) who were on site at the time.
Police said no further details of the pilot will be announced until a coroner’s inquest is opened.
Anyone with information relating to this incident is urged to contact Bedfordshire Police on the non-emergency 101 number.