Salient object detection provides an alternative solution to various image semantic understanding tasks such as object recognition, adaptive compression and image retrieval. Recently, low-rank matrix recovery (LR) theory has been introduced into saliency detection, and achieves impressed results. However, the existing LR-based models neglect the underlying structure of images, and inevitably degrade the associated performance. In this paper, we propose a Low-rank and Structured sparse Matrix Decomposition (LSMD) model for salient object detection. In the model, a tree-structured sparsity-inducing norm regularization is firstly introduced to provide a hierarchical description of the image structure to ensure the completeness of the extracted salient object. The similarity of saliency values within the salient object is then guaranteed by the $ell _infty$-norm. Finally, high-level priors are integrated to guide the matrix decomposition and enhance the saliency detection. Experimental results on the largest public benchmark database show that our model outperforms existing LR-based approaches and other state-of-the-art methods, which verifies the effectiveness and robustness of the structure cues in our model.