Anomaly detection is a challenging computer vision task in industrial scenario. Advancements in deep learning constantly revolutionize vision-based anomaly detection methods, and considerable progress has been made in both supervised and self-supervised anomaly detection. The commonly-used pipeline is to optimize the model by constraining the feature embeddings using a distance-based loss function. However, these methods work in Euclidean space, and they cannot well exploit the data lied in non-Euclidean space. In this paper, we are the first to explore anomaly detection task in hyperbolic space that is a representative of non-Euclidean space, and propose a hyperbolic anomaly detection (HypAD) method. Specifically, we first extract image features and then map them from Euclidean space to hyperbolic space, where the hyperbolic distance metric is employed to optimize the proposed HypAD. Extensive experiments on the benchmarking datasets including MVTec AD and VisA show that our HypAD approach obtains the state-of-the-art performance, demonstrating the effectiveness of our HypAD and the promise of investigating anomaly detection in hyperbolic space.