Recent studies have demonstrated the advantages of fusing information from multiple views for various machine learning applications. However, most existing approaches assumed the shared component common to all views and ignored the private components of individual views, which thereby restricts the learning performance. In this paper, we propose a new multi-view, low-rank, and sparse matrix decomposition scheme to seamlessly integrate diverse yet complementary information stemming from multiple views. Unlike previous approaches, our approach decomposes an input data matrix concatenated from multiple views as the sum of low-rank, sparse, and noisy parts. Then a unified optimization framework is established, where the low-rankness and group-structured sparsity constraints are imposed to simultaneously capture the shared and private components in both instance and view levels. A proven optimization algorithm is developed to solve the optimization, yielding the learned augmented representation which is used as features for classification tasks. Extensive experiments conducted on six benchmark image datasets show that our approach enjoys superior performance over the state-of-the-art approaches.