Disclosed is an apparatus for processing a lens edge. The apparatus comprises: a wheel-shaft-moving rotating member whose one end is fixed to a fixing frame by a moving-shaft, for moving pivotally about the moving-shaft; a wheel-shaft mounted on the other end of the wheel-shaft-moving rotating member, for moving pivotally with the wheel-shaft-moving rotating member and for being rotated by driving a wheel-rotating motor; and a cutter for processing the lens edge into a form of a step/incline shape, the cutter being coupled to one end of the wheel shaft to move with the wheel-shaft to contact the lens edge, and rotated with the wheel shaft to cut the surface of the lens, and the cutter comprising a rotating body inserted into the wheel-shaft to rotate with the wheel-shaft, and at least one cutting projection formed on the circumference of the rotating body to cut the edge and the periphery of the lens.