Anomaly detection on attributed networks has attracted a surge of research attention due to its broad applications in various high-impact domains, such as security, finance, and healthcare. Nonetheless, most of the existing efforts do not naturally generalize to unseen nodes, leading to the fact that people have to retrain the detection model from scratch when dealing with newly observed data. In this study, we propose to tackle the problem of inductive anomaly detection on attributed networks with a novel unsupervised framework: AEGIS (adversarial graph differentiation networks). Specifically, we design a new graph neural layer to learn anomaly-aware node representations and further employ generative adversarial learning to detect anomalies among new data. Extensive experiments on various attributed networks demonstrate the efficacy of the proposed approach.