The present invention relates to a high-pressure pump for a fuel injection device of an internal combustion engine, with a pump housing, with at least one work chamber disposed in the pump housing functionally between an inlet region and a supply region. A working element is movably disposed in the work chamber, and a pump shaft is provided in the pump housing by means of which the working element can be driven. In order to obtain a shortened structural length, and an extended service life of the pump, a provision is made that the pump housing can be fastened to a wall of a motor housing of the internal combustion engine, wherein the pump shaft can be radially supported against a shaft of the internal combustion engine, which shaft is supported in the motor housing.