This paper presents a simple yet effective method for anomaly detection. The main idea is to learn small perturbations to perturb normal data and learn a classifier to classify the normal data and the perturbed data into two different classes. The perturbator and classifier are jointly learned using deep neural networks. Importantly, the perturbations should be as small as possible but the classifier is still able to recognize the perturbed data from unperturbed data. Therefore, the perturbed data are regarded as abnormal data and the classifier provides a decision boundary between the normal data and abnormal data, although the training data do not include any abnormal data.Compared with the state-of-the-art of anomaly detection, our method does not require any assumption about the shape (e.g. hypersphere) of the decision boundary and has fewer hyper-parameters to determine. Empirical studies on benchmark datasets verify the effectiveness and superiority of our method.