Straub was born in the Netherlands in 1944 and moved to Germany in 1963, where he enrolled in the actor's school in Munich. After a couple of film roles, he focussed on writing and producing.
During the 1970s he regularly worked together with legends of German cinema, such as Rainer Werner Fassbinder, Wim Wenders, Volker Vogeler and Werner Herzog.
In 1970, Straub co-founded the Filmverlag der Autoren, a collective of young filmmakers of great influence in Germany. The Filmverlag organised all directors of the Neue Deutsche Film and released in just a few of years more than a hundred features.
During the 1980s, Straub produced several important German gay features, including the Rainer Werner Fassbinder-biography Ein Mann wie EVA (Radu Gabrea, 1984) and the controversial, awarded comedy Taxi zum Klo (Frank Ripploh, 1981). In 1979 he co-founded distribution venture Filmwelt. The company released in Germany among others Stephen Frears' My Beautiful Laundrette (1985) and Neil Jordan's Mona Lisa (1986).
In the 1980s and 1990s, he worked as a teacher at the Filmacademy of Baden-Württemberg.