Anomaly target detection is a research hotspot in hyperspectral imagery processing.Aiming at the problems of current anomaly target detection algorithms, a new anomaly target detection algorithm is proposed by combining low-rank tensor decomposition with sparse representation for hyperspectral imagery.The algorithm utilizes the spatial spectrum and spectral characteristics by solving the problems of background, anomaly target and noise in hyperspectral imagery.Firstly, the algorithm uses the low-rank tensor decomposition to restore the original hyperspectral imagery, so that the image quality is improved, and the anomaly target becomes prominent and easy to be detected.Then, the sparse difference index is used for anomaly target detection to obtain the required anomaly detection results.Finally, simulation experiments are carried out by using real hyperspectral images.The results show that the new anomaly target detection algorithm has the characteristics of high detection accuracy, low false alarm rate and good robustness.