A hyperspectral anomaly detection algorithm based on fractional Fourier transform (FrFT) and total variation regularization constraint was proposed aiming at the challenge of insufficient utilization of spatial information and contamination of background dictionary in low-rank and sparse representation based hyperspectral anomaly detection algorithms. The high-dimensional image data was mapped to multiple subspaces through the clustering algorithm. A pure background dictionary was obtained by constructing the FrFT-RX operator in order to enhance the discrimination between anomalies and background. A total variation regularization constraint was introduced into the low-rank and sparse representation model in order to describe the spatial features of background and anomalies in the intermediate domain after FrFT transformation. The optimal solution of the model was obtained by using the alternating direction method of multipliers. The anomaly detection results were obtained. The experimental results on three real hyperspectral datasets demonstrate that the proposed algorithm has a higher detection rate and a lower false alarm rate compared with the other five anomaly detection algorithms.