Biometric identification from three-dimensional (3-D) face surface characteristics has become popular. Traditional face recognition methods have achieved very high recognition accuracy under controlled environments. However, 3-D face recognition technology still faces a great challenge for facial expressions and missing data caused by pose variations or occlusions. The mesh-based scale-invariant feature transform (SIFT)-like method is one of the most effective methods to deal with these issues. However, eliminating edge response has not been considered in this kind of method, which affects recognition performance and computation cost. To address this problem, a mesh edge point filter is proposed to remove edge keypoints. For feature description, a local descriptor that is composed of the histogram of geometric shapes and the histogram of shape index is designed to describe local shapes of keypoints. A complete mesh-based SIFT-like framework for 3-D face recognition is also presented. Results from experiments based on the Bosphorus and face recognition grand challenge v2.0 databases show that the proposed method is effective for expression variations, occlusions, and pose variations. Compared with several state-of-the-art methods, the proposed method has obtained a great compromise between computational complexity and recognition performance.