An electric power supply system for driving an electric rotating machine has a generator supplied with driving power from an engine to generate alternating-current electric power and a matrix converter as an alternating-current to alternating-current direct converter supplied with the alternating-current electric power to output arbitrary alternating-current electric power. By driving a motor with the alternating-current electric power supplied from the matrix converter, only one time electric power conversion is carried out to provide high efficiency in the whole system. In addition, electric power loss can be reduced so as to enhance a motor output when the system is applied to a vehicle power supply system.