Recent years have witnessed a growing interest in developing methods for 3D face recognition. However, 3D scans often suffer from the problems of missing parts, large facial expressions, and occlusions. To be useful in real-world applications, a 3D face recognition approach should be able to handle these challenges. In this paper, we propose a novel general approach to deal with the 3D face recognition problem by making use of multiple keypoint descriptors (MKD) and the sparse representation-based classification (SRC). We call the proposed method 3DMKDSRC for short. Specifically, with 3DMKDSRC, each 3D face scan is represented as a set of descriptor vectors extracted from keypoints by meshSIFT. Descriptor vectors of gallery samples form the gallery dictionary. Given a probe 3D face scan, its descriptors are extracted at first and then its identity can be determined by using a multitask SRC. The proposed 3DMKDSRC approach does not require the pre-alignment between two face scans and is quite robust to the problems of missing data, occlusions and expressions. Its superiority over the other leading 3D face recognition schemes has been corroborated by extensive experiments conducted on three benchmark databases, Bosphorus, GavabDB, and FRGC2.0. The Matlab source code for 3DMKDSRC and the related evaluation results are publicly available at http://sse.tongji.edu.cn/linzhang/3dmkdsrcface/3dmkdsrc.htm.