Curvelet transform can describe the signal by multiple scales, and multiple directions. In order to improve the performance of 3D face recognition algorithm, we proposed an Anthropometric and Curvelet features fusion-based algorithm for 3D face recognition (Anthropometric Curvelet Fusion Face Recognition, ACFFR). First, the eyes, nose, and mouth feature regions are extracted by the Anthropometric characteristics and curvature features of the human face. Second, Curvelet energy features of the facial feature regions at different scales and different directions are extracted by Curvelet transform. At last, Euclidean distance is used as the similarity between template and objectives. To verify the performance, the proposed algorithm is compared with Anthroface3D and Curveletface3D on the Texas 3D FR database. The experimental results have shown that the proposed algorithm performs well, with equal error rate of 1.75% and accuracy of 97.0%. The algorithm we proposed in this paper has better robustness to expression and light changes than Anthroface3D and Curveletface3D.