Bill Greever is a former NASCAR driver from Bluefield, WV. He competed in two Nextel Cup Series events in his career. He debuted in 1949, racing in the inagural event at North Wilkesboro. Starting positions in the field of twenty-two are unknown, but Greever failed to finish the event and ended up 18th. Greever's other race came in 1950, when he was able to slightly improve at Martinsville. Starting positions in the field of twenty-five car field are unknown, but Greever fell just a few laps down and drove to a career-best 17th place showing.