Dempsey was born in Los Angeles. He started racing back in the mid 1940's. There are photos of him racing jalopies at Presott Raceway in 1946.
He raced midgets before attempting to qualify for the Indy 500 in 1956. Driving from the Martin Brothers he failed to qualify. He DNQ'd again the next year still driving for the Martin Brothers.
In 1958 he qualified in the Sorenson Kuzma/Offy but retired after a refuelling fire. The following year he attempted to qualify the Novi Diesel but without success.
IN 1960 Jimmy Daywalt qualified the Bryant Heating & Cooling KK500G/Offy, but declined to race as he said the car was unsafe. Dempsey Wilson disagreed and was allowed to drive. He started on the back of the grid and went out early on with electrical problems.
In 1961 driving the Lysle Greenman Kuzma/Offy he failed to finish due to a fuel pump and at his last visit to the Brickyard in 1963 he drove the Vita Fresh Orange Juice Kuzma/Offy to 11th place. His best finish at Indy.
He started a camshaft manufacturing business, Dempsey Wilson Racing Camshafts, after he retired from driving and sadly died of leukaemia in 1971.
Seth Wilson, Dempsey's Grandson currently races stockcars.