The two-seater plane, a Mark IV Jet Provost, ploughed into the ground at Woolaston, near Lydney, in the Forest of Dean, reportedly just two miles from the Oldbury and Berkeley nuclear power plants.
Police said the plane, which came down in a field of wheat just a few hundred yards from the River Severn and a railway line, had burst into flames on impact.
The victims have not been named. Police said the pilot who died was a man, 43, from Sussex. The passenger is believed to come from Worcester.
The privately-owned plane had taken off from Gloucestershire airport, Staverton, between Gloucester and Cheltenham.
The pilot had been giving pleasure flights over the weekend for members of a local flying club.
Officials from the Air Accident Investigation Board at Farnborough will conduct an inquiry into the crash.