The son of a Benelli employee, he began his racing career as a privateer Benelli racer. He made his Grand Prix debut as a Benelli factory rider in 1959. His best year was in 1969 when he finished second to Giacomo Agostini in the 350cc world championship. In 1971, Grassetti won the 250cc Austrian and Belgian Grand Prix races, but inconsistent results relegated him to only seventh place in the championship. He retired in 1974 after suffering serious injuries at the Spa-Francorchamps circuit in Belgium. Grassetti won three Grand Prix races in his career.