Anomaly detection of hyperspectral data has been gaining particular attention for its ability in detecting targets in an unsupervised manner. Autoencoder (AE), together with its variants can not only extract intrinsic features automatically but also detect anomalies that differ dramatically from others. Many AE-driven algorithms are, thus, proposed for anomaly detection in hyperspectral imagery (HSI), but they suffer from two problems: 1) when there exist anomalies in the training set, AE can generalize so well that it can also learn the abnormal patterns well, thereby reducing the ability to distinguish anomalies from the background and 2) geometric structure among samples are lost in latent space of AE, which is vital in hyperspectral anomaly detection. To tackle these problems, we propose a robust anomaly detector based on the AE framework, named robust graph AE (RGAE) detector, in this article. To be specific, we propose a robust AE framework with <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\ell _{2,1}$ </tex-math></inline-formula> -norm that is robust to noise and anomalies during training. Meanwhile, we embed a superpixel segmentation-based graph regularization term (SuperGraph) into AE. This strategy can preserve the geometric structure and the local spatial consistency of HSI simultaneously and also effectively reduce the searching space and execution time for each pixel. Extensive experiments are conducted on five datasets, and the results demonstrate that our method has a better detection performance, after comparing with other state-of-the-art hyperspectral anomaly detectors.