Face recognition is among the most popular biometric approaches due to its low intrusiveness and high uniqueness. However, recent face recognition algorithms such as sparse representation-based classification algorithms, often ignore the noises during training process. When training samples are corrupted, recognition performance will significantly degenerate. Therefore, face recognition is an active yet challenging topic in computer vision application. To solve this problem, this paper proposes a novel low-rank relaxed collaborative representation algorithm which is combined with global and local features. The low-rank decomposition algorithm separates sparse noise from training samples to get more effective face information. Suppressing the effect of sparse noise is essential for face recognition system. Meanwhile, considering the fact that the different features in a sample should contribute differently to the pattern classification, this paper uses relaxed collaboration representation to get more discriminating coding coefficients. The discrimination of face recognition system will be enhanced. In addition, combining local features with global features can further improve the recognition rate. The proposed algorithm contains all of the above advantages. Experimental results on face databases show that, although both training and testing image data might be corrupted due to occlusion and disguise, the proposed algorithm is very competitive with state-of-the-art recognition approaches on effectiveness and robustness.