Anomaly detection in dynamic graphs becomes very critical in many different application scenarios, e.g., recommender systems, while it also raises huge challenges due to the high flexible nature of anomaly and lack of sufficient labelled data. It is better to learn the anomaly patterns by considering all possible features including the structural, content and temporal features, rather than utilizing heuristic rules over the partial features. In this paper, we propose AddGraph, a general end-to-end anomalous edge detection framework using an extended temporal GCN (Graph Convolutional Network) with an attention model, which can capture both long-term patterns and the short-term patterns in dynamic graphs. In order to cope with insufficient explicit labelled data, we employ the negative sampling and margin loss in training of AddGraph in a semi-supervised fashion. We conduct extensive experiments on real-world datasets, and illustrate that AddGraph can outperform the state-of-the-art competitors in anomaly detection significantly.