A rear wheel steering apparatus may include: a driving part housed in a housing part; a rotating part rotated by the driving part; a moving shaft part connected to tie rods, and screwed to the rotating part; a spline plate spline-coupled to the moving shaft part so as to restrict rotation of the moving shaft part; and a space maintaining part protruding from the moving shaft part or the spline plate, and maintaining a space between the moving shaft part and the spline plate.