Anomaly detection plays a more and more important role in the hyperspectral image (HIS) processing field. Since the low-rank and sparse matrix decomposition (LRaSMD) algorithm can separate the anomalies from the background, it can protect the background model from corruption by anomalies and noises. A novel hyperspectral anomaly detection algorithm is proposed based on low-rank and sparse matrix decomposition-sparse representation (LRaSMD-SR). First, the relatively pure background is obtained by LRaSMD. Then, the background dictionary model is constructed from the pure background by means of sparse representation. Finally, the reconstruction error is employed to detect the anomalies. The effective experimental tests are conducted using both simulated and real datasets, and the experimental results show that the proposed LRaSMD-SR algorithm possesses a very promising performance of anomaly detection.