3D face recognition with the availability of only partial data (missing parts, occlusions and data corruptions) and single training sample is a highly challenging task. This paper presents an efficient 3D face recognition approach to address this challenge. We represent a facial scan with a set of local Keypoint-based Multiple Triangle Statistics (KMTS), which is robust to partial facial data, large facial expressions and pose variations. To address the single sample problem, we then propose a Two-Phase Weighted Collaborative Representation Classification (TPWCRC) framework. A class-based probability estimation is first calculated based on the extracted local descriptors as a prior knowledge. The resulting class-based probability estimation is then incorporated into the proposed classification framework as a locality constraint to further enhance its discriminating power. Experimental results on six challenging 3D facial datasets show that the proposed KMTS-TPWCRC framework achieves promising results for human face recognition with missing parts, occlusions, data corruptions, expressions and pose variations.