Title: ASGNN: Graph Neural Networks with Adaptive Structure. Abstract: The graph neural network (GNN) has presented impressive achievements in numerous machine learning tasks. However, many existing GNN models are shown to be extremely vulnerable to adversarial attacks, which makes it essential to build robust GNN architectures. In this work, we propose a novel interpretable message passing scheme with adaptive structure (ASMP) to defend against adversarial attacks on graph structure. Layers in ASMP are derived based on optimization steps that minimize an objective function that simultaneously learns the node feature and the graph structure. ASMP is adaptive in the sense that the message passing process in different layers is able to be carried out over different graphs. Such a property allows more fine-grained handling of the noisy graph structure and hence improves the robustness. Integrating ASMP with neural networks can lead to a new family of GNNs with adaptive structure (ASGNN). Extensive experiments on semi-supervised node classification tasks demonstrate that the proposed ASGNN outperforms the state-of-the-art GNN architectures with respect to classification performance under various graph adversarial attacks.