Since the face images might be not over-complete and they might be also corrupted under different viewpoints or different lighting conditions with noise, an efficient and effective method for Face Recognition (FR) was proposed, namely Robust Principal Component Analysis with Collaborative Representation based Classification (RPCA_CRC). Firstly, the face training dictionary D₀ was decomposed into two matrices as the low-rank matrix D and the sparse error matrix E; Secondly, the test image could be collaboratively represented based on the low-rank matrix D; Finally, the test image was classified by the reconstruction error. Compared with SRC (Sparse Representation based Classification), the speed of RPCA_CRC on average is 25-times faster. Meanwhile, the recognition rate of RPCA_CRC increases by 30% with less training images. The experimental results show the proposed method is fast, effective and accurate.