The aircraft went down in the area of FM 407 and Graham Road near the airstrip off Dillavou Lane.
The victim was an 86-year-old man.
The FAA described the plane as a single-seat 1936 Rose Parakeet A-1 biplane.
It’s not clear what caused the plane to go down.
The Federal Aviation Administration and the National Traffic Safety Board have been notified and will be conducting an investigation into the crash.
The NTSB said it will be in charge of the investigation.
New Fairview is about 30 miles northwest of Fort Worth.