By representing a test sample with a linear combination of training samples, sparse representation-based classification (SRC) has shown promising performance in many applications such as computer vision and signal processing. However, there are several shortcomings in SRC such as 1) the l(2)-norm employed by SRC to measure the reconstruction fidelity is noise sensitive and 2) the l(1)-norm induced sparsity does not consider the correlation among the training samples. Furthermore, in real applications, face images with similar variations, such as illumination or expression, often have higher correlation than those from the same subject. Therefore, we correspondingly propose to improve the performance of SRC from two aspects by: 1) replacing the noise-sensitive l(2)-norm with an M-estimator to enhance its robustness and 2) emphasizing the sparsity in terms of the number of classes instead of the number of training samples, which leads to the structured sparsity. The formulated robust structured sparse representation (RGSR) model can be efficiently optimized via alternating minimization method under the half-quadratic (HQ) optimization framework. Extensive experiments on representative face data sets show that RGSR can achieve competitive performance in face recognition and outperforms several state-of-the-art methods in dealing with various types of noise such as corruption, occlusion and disguise.