An extension of the ICP (Iterative Closest Point) registration algorithm based on modified M-estimation for realization of robustness against outlying gross noise in two point data sets. The proposed algorithm is utilized to obtain a transformation consisting of rotation and translation parameters in order to perform the best fit between the data sets. An objective function which includes independent residual components for each of xyz coordinates is defined to evaluate the fit between the data sets, taking account of distribution of the outlying noise, which occurs due to occlusion, shadowing, or highlighting in measurement. The approach is based on modifid M-estimation through an iterative procedure for optimization of the transform for correspondence. Some fundamental experiments utilizing real data of 2D and 3D measurement show effectiveness of the proposed method.