The fuel injection system has a high-pressure pump that delivers fuel to an accumulator and fuel supply pump delivers fuel to the suction side of the high-pressure pump, with a fuel metering unit between the fuel supply and high-pressure pumps to variably adjust the fuel quantity taken in by the high-pressure pump. The accumulator is connected to at least one fuel injector and a return leads from the fuel injector(s). The fuel return from the injector(s) feeds into the connection between the fuel supply pump and the fuel metering unit. A connection controlled by a pressure valve leads from the fuel return to a discharge region. The high-pressure pump only draws fuel from the fuel return in operating states in which the fuel quantity delivered by the fuel supply pump is less than the required intake quantity of the high-pressure pump.