The plane was attempting to land, but pulled back up at the end of the runway.
"It attempted to abort the landing and take off again," Sgt. F.L. Tyler of the Virginia State Police told reporters. "It then went off the south end of the runway and then landed in the tree line."
When the plane struck the trees, it immediately caught fire, officials said.
Rescue workers recovered all six bodies from the burned wreckage.
The identities of the victims have not been released, but police said they were all from out of state.
The cause of the crash is under investigation. Officials with the National Transportation Safety Board, Federal Aviation Administration and five rescue and fire crews were on the scene.