Autoencoder can not only extract features in an unsupervised manner, but also selects samples out that differs significantly from others. However, autoencoder is sensitive to noise and anomalies during training, and the relationships between pixels are discarded. In order to tackle these problems, we propose a robust graph autoencoder (RGAE) for hyperspectral anomaly detection. To be specific, we first redesign the objective function to encourage the network more robust to noise and anomalies. Meanwhile, a superpixel segmentation-based graph regularization term (SuperGraph) is incorporated into AE to preserve the geometric structure and spatial information simultaneously. Experiments with three real data sets are conducted to evaluate the performance, and the detection results demonstrate that our method outperforms other state-of-the-art hyperspectral anomaly detectors.