An electric-oil pressure power steering system for a vehicle is described which comprises an oil pump driven by an electric motor for supplying power fluid to a power cylinder, a steering wheel connected to a control valve for controlling the supply of the power fluid, and an electronic switching device for controlling the supply of electric power to said motor in response to the change of a vehicle speed, said electronic switching device including a means for controlling continuously the supply of the electric power and a means for controlling discontinuously or variably the supply of the electric power.