The invention discloses a reactor pressure vessel bottom head penetration piece outer wall inspection apparatus. The apparatus comprises a self-adaptive mechanism used for arranging an eddy current probe and allowing the eddy current probe to always cling to a penetration piece and a bottom head when the eddy current probe rotates around the penetration piece, a first axial driving mechanism for driving the self-adaptive mechanism to move along the axial direction of the penetration piece, a first circumferential driving mechanism for driving the self-adaptive mechanism to move along the circumferential direction of the penetration piece, and a first positioning mechanism for realizing positioning of the outer wall inspection apparatus. The outer wall inspection device has a compact structure and a small size, can be easily and accurately sleeved on the outer wall of the penetration piece or can enter the penetration piece under the driving of an operating platform in order to carry out scanning, and does not generate too large transverse overturning force on the penetration piece due to its small volume weight if the inspection device shakes; and the self-adaptive mechanism of the outer wall inspection device can guarantee that the eddy current probe always clings to the bottom head and the penetration piece in the scanning process in order to obtain accurate inspection data.