To provide a motor driving system for an electrically powered automotive vehicle, in which the drive motor is rotationally controlled to increase the reliability, the use is made of an angle sensor for detecting the relative rotational angle between a stator and a rotor of a drive motor for driving the electric vehicle and a controller for controlling the rotation of the drive motor on the basis of the relative rotational angle detected by the angle sensor. The angle sensor is provided in a plural number. The controller includes an angle sensor switching unit operable to select and activate one of the plurality of the angle sensors and then to switch over to an activation of another one of the angle sensors in the event that the one of the angle sensors is determined abnormal.