Anomaly detection aims at locating the spectral different objects of a specific scene without any prior information, and has gained increasing attention. By decomposing the input hyperspectral image (HSI) into a background tensor and an anomaly tensor, the tensor approximation is an efficient tool for detecting the anomalies. Low rankness is usually utilized as the regularizer during the background reconstruction process. Different from most existing hyperspectral anomaly detection methods which compute the truncated nuclear norm of the third folding of the original HSI, a novel weighted‐sparsity‐regularized tensor linear representation (WsrTLR) method is proposed for hyperspectral anomaly detection in this paper. Tensor linear representation is utilized to formulate the background HSI by a three‐dimensional (3D) representation base and the corresponding 3D representation coefficient. Low rankness is applied to constrict the representation coefficient, an operation which avoids destroying the multi‐way structure and losing information during the matrixing process, and ensures a satisfactory detection accuracy. Meanwhile, by incorporating the weighted‐sparsity‐regularized tensor linear representation to reconstruct the background tensor, the anomalies can be easily detected by eliminating the background tensor from the original scene. In addition, to avoid negative influence caused by the redundant bands and noisy bands in the representation process, informative bands have been first selected via an optimal neighborhood reconstruction strategy. Experimental results and data analysis on four real hyperspectral datasets, which contain anomalies with different sizes, have demonstrated the effectiveness of the proposed�method.