An electric power steering apparatus comprises a steering assisting electric motor having an output shaft and a speed reduction mechanism. The speed reduction mechanism includes conical first and second gears to be engaged with each other. The first and second gears include a plurality of teeth each having a tooth surface. The mutually corresponding tooth surfaces of the first and second gears each include engaging regions to be engaged with each other. A center position in a tooth width direction of the engaging region of each tooth surface of the first gear in an unloaded state is offset by a first offset amount from center position in the tooth width direction of the tooth surface of the first gear to a relatively small end portion of the tooth of the first gear. A center position in a tooth width direction of the engaging region of each tooth surface of the second gear in an unloaded state is offset by a second offset amount from a center position in the tooth width direction of the tooth surface of the second gear to a relatively small end portion of the tooth of the second gear.