A power seat driving apparatus for a vehicle includes a moving unit and a decelerating mechanism. The deceleration mechanism includes a driving gear, a driven gear engaging with the driving gear and driven to rotate while decelerating a rotational speed of the driving gear, a supplemental gear coaxially connected to the driven gear in an interlocking manner, made of a resin material having elasticity and lower rigidity than the driven gear, having a larger tooth thickness than a tooth thickness of the driven gear by an amount corresponding to a backlash, and engaging the driving gear together with the driven gear, and a housing accommodating and rotatably supporting the driving gear, the driven gear and the supplemental gear.