The classical RX anomaly detection operator assumes that the background data information conforms to Gaussian distribution, but the hyperspectral image is degraded due to a large amount of additive noise, and the background information does not conform to this kind of distribution. To solve this problem, the algorithm of RX anomaly target detection for hyperspectral imagery based on low-rank tensor decomposition is proposed. Firstly, the low rank tensor decomposition method is introduced to recover the hyperspectral image, and which uses the tensor data structure and low rank data characteristics of hyperspectral image, so that the anomaly target information becomes prominent compared with the complex background information, and then the RX anomaly detection operator is used to detect the anomaly target in the recovered hyperspectral image; Finally, the anomaly target detection results are obtained. Through the comparison of simulation experiments, the new anomaly target detection method has the characteristics of high detection accuracy, low false alarm rate and good robustness.