The abundant information in the graph helps us to learn more expressive node representations. Different nodes in the neighborhood bring different information. Average weight aggregation in most Graph Neural Networks fails to distinguish such difference. GAT-based models introduce attention mechanism to solve this problem. However, this attention mechanism they introduced only considers the similarity between node features, and ignores the rich structural information contained in the graph structure to some degree. In addition, for each node, we need specific encoder to aggregate the distinguishing information from the neighborhood. In this paper, we propose Graph Neural Networks with Structural Adaptive Receptive fields (STAR-GNN), which generates a learnable receptive field with local structure for each node. Further, STAR-GNN preserves not only the simple tree-like graph structure of each node, but also the induced subgraph of the central node and the learnt receptive field. Experimental results demonstrate the power of STAR-GNN in learning local-structural receptive fields adaptively and encoding more informative structural characteristics in graph neural networks.