A ball screw mechanism comprises a screw shaft, a nut and balls. The nut has a cylindrical portion in the axial middle on the outer peripheral surface thereof that becomes a fitting surface for fitting in a sleeve, and small diameter step portions in the opposite axial sides on the outer peripheral surface thereof that become non-fitting surfaces not fitting in the sleeve. A portion of a wheel steering shaft is provided with the screw shaft, and a plurality of balls are disposed in a rolling way defined between a thread groove formed in the outer periphery of the screw shaft and a thread groove formed in the inner periphery of the nut.