Graph deep learning models, such as graph convolutional networks (GCN) achieve remarkable performance for tasks on graph data. Similar to other types of deep models, graph deep learning models often suffer from adversarial attacks. However, compared with non-graph data, the discrete features, graph connections and different definitions of imperceptible perturbations bring unique challenges and opportunities for the adversarial attacks and defenses for graph data. In this paper, we propose both attack and defense techniques. For attack, we show that the discreteness problem could easily be resolved by introducing integrated gradients which could accurately reflect the effect of perturbing certain features or edges while still benefiting from the parallel computations. For defense, we observe that the adversarially manipulated graph for the targeted attack differs from normal graphs statistically. Based on this observation, we propose a defense approach which inspects the graph and recovers the potential adversarial perturbations. Our experiments on a number of datasets show the effectiveness of the proposed methods.