He began studies at the Netherlands Film and Television Academy in 1961, and released his first movie in 1966, De minder gelukkige terugkeer van Joszef Katus naar het land van Rembrandt.

He joined the editorial staff of the film magazine Skoop in 1963, working alongside Nikolai van der Heyde, Gied Jaspars, and Pim de la Parra.

After the demise of Scorpio Films, Verstappen directed two films based on novels by Simon Vestdijk, Pastorale 1943 (1978) and Het verboden bacchanaal (1981).

While the first was a commercial success, drawing an audience of over a million, the second film flopped, as did two later films, De Zwarte Ruiter (1983) and De Ratelrat (1987).

In 1992 he was awarded the Dutch Filmmuseum Award for his contributions to the Dutch film industry, and in 1995 he received a Golden Calf for his body of work.