The accuracy of anomaly detection in hyperspectral images (HSIs) faces great challenges due to the high dimensionality, redundancy of data, and correlation of spectral bands. In this paper, to further improve the detection accuracy, we propose a novel anomaly detection method based on texture feature extraction and a graph dictionary-based low rank decomposition (LRD). First, instead of using traditional clustering methods for the dictionary, the proposed method employs the graph theory and designs a graph Laplacian matrix-based dictionary for LRD. The robust information of the background matrix in the LRD model is retained, and both the low rank matrix and the sparse matrix are well separated while preserving the correlation of background pixels. To further improve the detection performance, we explore and extract texture features from HSIs and integrate with the low-rank model to obtain the sparse components by decomposition. The detection results from feature maps are generated in order to suppress background components similar to anomalies in the sparse matrix and increase the strength of real anomalies. Experiments were run on one synthetic dataset and three real datasets to evaluate the performance. The results show that the performance of the proposed method yields competitive results in terms of average area under the curve (AUC) for receiver operating characteristic (ROC), i.e., 0.9845, 0.9962, 0.9699, and 0.9900 for different datasets, respectively. Compared with seven other state-of-the-art algorithms, our method yielded the highest average AUC for ROC in all datasets.