Abstract: A novel 3D face recognition algorithm using geometry and local shape descriptors was proposed to overcome the influence of expression variations. At first, multiscale shape variation indexes were calculated to locate keypoints on the 3D face. Then, a two-step matching method was proposed to improve the efficiency: a large number of irrelevant candidate faces were eliminated based on the extracted 3D histograms of normal distributions at first and then the keypoints of the remaining faces were matched based on the covariance matrix descriptor generated as local shape descriptors. Finally, the similarity of two faces was measured by the number of the keypoints that can be correctly matched. The experiments of the proposed algorithm were carried out on the Bosphorus, FRGC v2.0 and BU-3DFE datasets and achieved superior recognition performance. The results demonstrate that the proposed algorithm is robust to expression variations and outperforms the state-of-the-art algorithms in term of the recognition speed.