Automatic registration for 3D shapes is an attractive problem in computer vision. Various registration algorithms based on different surface representations have been developed for this topic. However, most of the existing algorithms suffer from some limitations mainly related to discriminating similarity metric, partially overlapping data, and the robustness to resolution, noise and occlusion. In this research, hybrid dimensionality-reduction shape descriptions (DRSD) are proposed for pair-wise registration, which aims to overcome these limitations. Based on recently emerging angle-preserving parameterization techniques such as Harmonic Maps and ABF++, 3D shapes are described in low-dimension space with both local and global considerations. Therefore, searching for correspondences, verifying overlapping regions and calculating registration error all can be implemented in low-dimension space. Moreover, a large number of experiments, using both real and synthetic images, have been carried out to show the accuracy, efficiency and robustness of the hybrid DRSD algorithm.