A fuel injector (3) has a plunger (7) with an oblique control edge (12). The plunger (7) is driven by a drive unit (20) which is acted upon by fluid pressure separate from the fuel system. The plunger (7) is rotatable around its longitudinal central axis (8) by means of a setting device (60). A control device (31) regulates the inflow and outflow of fluid pressure to a double acting piston (22) of the drive unit (20). A signal for beginning an injection cycle is given by an electric pulse generator (40) or a control camshaft (61) of the control device (31). A return piston (34) of the control device (31) is acted on by fuel pressure and is connected through a line (33) with a pump chamber (6) of the fuel injector (3). At the end of the injection cycle the control edge (12) opens a passage (14) to pressure in the pump chamber (6 ) and a pressure surge acts through the line (33) on the return piston (34).