A variable transmission ratio steering apparatus for a vehicle is configured with an input shaft coupled to a steering wheel of the vehicle, a sensor for sensing a rotation angle of the input shaft, an output shaft operatively linked to steerable road wheels of the vehicle, an actuator having an electric motor which is configured to vary a transmission ratio between a rotation angle of the output shaft and the rotation angle of the input shaft, and a controller. More specifically, the controller includes a desired rotation angle calculation unit, a difference calculation unit, and a difference limitation unit, whereby a rotation angle of a rotor of the electric motor is limited. With such a configuration, a rotation speed of the rotor of the electric motor can be limited by limiting the rotation angle of the rotor, and consequently, audible operation noises arising from the electric motor can be minimized.