A high-pressure pump having a rotationally driven drive shaft and at least one pump element which has a pump piston driven at least indirectly in a reciprocating motion by the drive shaft which piston is guided in a cylinder bore and with its end remote from the drive shaft defines a pump work chamber. The pump piston is braced at least indirectly on the drive shaft. Extending through the pump piston is at least one line which discharges at the circumference of the pump piston in the cylinder bore spaced apart from the end of the pump piston that defines the pump work chamber and which leads toward the drive shaft to the region where the pump piston is braced.