Officials confirmed the crash happened around 12:45 p.m. and estimated that six people were on board.
The plane was described as a single-engine, Beechcraft Bonanza.
The plane's owner said engine trouble was to blame.
The pilot, Michael Weeks of Benson, had to land the plane in brush just east of the runway's edge.
The aircraft ascended 40 feet off the ground before it crashed, authorities said on Saturday.
No one was injured.
"The pilot set it down. The passengers on, and him, were fine, and they walked away which is fine, "said Airport Manager Stanley Bass. "The engine sputtered. He lost some power, and he set it back down."
Weeks said he was flying people to NASCAR races in Darlington, South Carolina, and said the engine started to skip after he took off.
Despite the problem, airport officials said the plane is a dependable aircraft.
"If you were going to compare it with a car, it would be a Cadillac. Nice plane," said Bass.
It was unclear how much damage the crash caused. FAA officials are due Monday to examine the wreck.