Graph Convolutional Networks (GCNs) achieved tremendous success by effectively gathering local features for nodes. However, commonly do GCNs focus more on node features but less on graph structures within the neighborhood, especially higher-order structural patterns. However, such local structural patterns are shown to be indicative of node properties in numerous fields. In addition, it is not just single patterns, but the distribution over all these patterns matter, because networks are complex and the neighborhood of each node consists of a mixture of various nodes and structural patterns. Correspondingly, in this paper, we propose Graph Structural topic Neural Network, abbreviated GraphSTONE 1, a GCN model that utilizes topic models of graphs, such that the structural topics capture indicative graph structures broadly from a probabilistic aspect rather than merely a few structures. Specifically, we build topic models upon graphs using anonymous walks and Graph Anchor LDA, an LDA variant that selects significant structural patterns first, so as to alleviate the complexity and generate structural topics efficiently. In addition, we design multi-view GCNs to unify node features and structural topic features and utilize structural topics to guide the aggregation. We evaluate our model through both quantitative and qualitative experiments, where our model exhibits promising performance, high efficiency, and clear interpretability.