Traditional anomaly detection algorithms for hyperspectral imagery does not consider spatial information of imagery, which decreases detection efficiency of anomaly detection. The traditional RXD algorithm uses Gauss model to evaluate the distribution of background, but ignores spatial correlation of the imagery. Aiming at improving detection efficiency, this paper proposed an anomaly detection algorithm which utilize both spatial and spectral information of hyperspectral imagery based on graph Laplacian. In this paper, an anomaly detection algorithm for hyperspectral imagery based on graph Laplacian (Graph Laplacian Anomaly Detection with Mahalanobis distance, LADM) is presented. The spatial information is considered in the model by graph Laplacian matrix. First, LADM considers not only spectral information but also the spatial information by mapping image to a graph. Secondly, a symmetrical normalization Laplacian matrix is constructed for the graph with Mahalanobis distance. The operation eliminates interference among the nodes, which improves the accuracy of Laplacian matrix and improves the detection result. Thirdly, LADM detectors is constructed with graph Laplacian detection model. Lastly, anomaly detection model based on graph is given based on graph Laplacian and spectral vector of the pixels. A threshold value is given to judge whether the currently detection pixel is anomaly or not. Experiments for synthetic data and real hyperspectral image is proposed in this paper. The proposed algorithm is compared with three classical anomaly detection algorithms. ROC curves and AUC values are given for both synthetic data and real data in the paper. Experiments results show that LADM algorithm can improve the accuracy of anomaly detection for hyperspectral imagery, and reduced the false alarm rate.