Wilson was born in Los Angeles, California. He drove in the USACChampionship Car series, racing in the 1956, 1958–1965 and 1968–1969 seasons with 32 starts, including the Indianapolis 500 races in 1958, 1960, 1961, and 1963. He finished in the top ten 4 times, with his best finish in 8th position in 1960 at Milwaukee. Outside of racing, Wilson owned a business called "Dempsey Wilson Racing Cams", which refurbished camshafts. He died in his home city of Los Angeles.
The Indianapolis 500 was part of the FIA World Championship from 1950 through 1960. Drivers competing at Indy during those years were credited with World Championship points and participation. Dempsey Wilson participated in 2 World Championship races but scored no World Championship points.