An electric power steering apparatus includes a pinion shaft coupled to a steering wheel shaft, a rack shaft coupled to the pinion shaft and having a ball screw, a ball nut provided in the ball screw through a plurality of balls, a first pulley coupled to the ball nut, a torque sensor sensing steering wheel torque, an electric motor for generating a steering assisting force according to the torque sensor signal, a second pulley at one end of the electric motor, and a belt connecting the first pulley to the second pulley to transmit the steering assisting force to the ball nut. The first or second pulley have a coating including 10 to 90 wt % molybdenum sulfide, 5 to 10 wt % antimony trioxide, 1 to 5 wt % antirust agent, 1 to 5 wt % auxiliary lubricant, and 1 to 3 wt % organic adhesive in a 1 to 10 wt % solvent.