In recent years, with the popularization of Web 2.0, people pay more and more attentions to the graph anomaly detection. The graph anomaly detection plays an increasingly vital role in the field of fraud detection, intrusion detection, false voting, and zombie fan analysis. This paper presents a survey on existing approaches to address this problem and reviews the recent developed techniques to detect graph anomalies. The graph-oriented anomaly detection is divided into two types, the anomaly detection on static graph and the anomaly detection on dynamic graph. Existing work on static graph anomaly detection have identified two types of anomalies:One is individual anomaly that refers to the abnormal behaviors of individual entity, the other is group anomaly that occurs due to unusual patterns of groups. The anomaly on dynamic graph can be divided into three types:Isolated individual anomaly, group anomaly, and event anomaly. This paper introduces the current research progress of each kind of anomaly detection methods, and summarizes the key technologies, common frameworks, application fields, common data sets, and performance evaluation methods of graph-oriented anomaly detection. Finally, future research directions on graph anomaly detection are discussed.