In 1967, Graves was recruited by Desilu Studios to replace Steven Hill as the lead actor on Mission: Impossible. Graves portrayed the iconic character of Jim Phelps, the sometimes-gruff director of the Impossible Missions Force, for the six following seasons of the series.
After the series ended in 1973, Graves played a cameo-type support role in the feature film Sidecar Racers in Australia which was released in 1975. Graves also made a guest appearance in the teen soap opera Class of 74 in mid-1974, playing himself.
