The fuel injection system has a high-pressure pump which pumps fuel into a reservoir to be supplied to injectors disposed at the engine cylinders. A feed pump supplies fuel to the high-pressure pump. The high-pressure pump has at least one pump element including a pump piston that defines a work chamber and is driven in a reciprocating motion; the work chamber has a communication with the compression side of the feed pump, in which an intake valve opening toward the work chamber is disposed, and through which valve fuel flows into the work chamber upon the intake stroke of the pump piston. The intake valve has a valve member, which is urged in a closing direction by a closing spring, and the closing spring is braced at least indirectly on the pump piston; with an increasing intake stroke of the pump piston, the closing force exerted on the valve member by the closing spring becomes less. A minimal opening differential pressure of the intake valve is less than 0.9 bar.