Disclosed is an electric power steering system including a housing; a steering shaft positioned in the housing; a worm wheel mounted on the steering shaft; a worm shaft; a worm gear formed on the worm shaft so as to mesh with the worm wheel; a motor for driving the worm shaft; a first worm shaft bearing positioned on an end of the worm shaft; and an elastic member for applying a load to the first worm shaft bearing in a diametric direction, the elastic member being formed by double-folding a leaf spring in an approximately U-shaped configuration, both ends of the elastic member being supported by the housing, a central portion of the elastic member abutting an outer peripheral surface of the first worm shaft bearing.