The incident happened on Back Lane in Farsley at around 9.40pm on Friday, July 20.
The adult male who was driving the quad bike was airlifted to hospital with serious injuries after he became trapped under a white van following the collision.
A spokesperson for West Yorkshire Police said: "A collision was reported on Back Lane near the Old Hall Hotel in Farley at 9.40pm on Friday.
"A quad bike collided with a white Transit van and the adult male driver of the quad bike became trapped under the van.
"He was airlifted to hospital with serious injuries."