A ball bearing 34 serving as a support reference for a pinion shaft 2 is located directly under a worm wheel 51. Thus, even when a temperature change occurs around the electric power steering apparatus, the engagement position between the worm wheel 51 and the worm 53 shifts only slightly in the axial direction of the pinion shaft 2. Furthermore, a bearing hole 47 into which an outer race of a lower needle bearing 36 is pressed and a bearing hole 45 into which an outer race of an upper ball bearing 34 is pressed are formed in a common lower gear box 41, and can be fabricated by through processing using a boring tool from the bearing hole 45 side.