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In this work, we address semi-supervised classification of graph data, where the categories of those unlabeled nodes are inferred from labeled nodes as well as graph structures. Recent works often solve this problem via advanced graph convolution in a conventionally supervised manner, but the performance could degrade significantly when labeled data is scarce. To this end, we propose a Graph Inference Learning (GIL) framework to boost the performance of semi-supervised node classification by learning the inference of node labels on graph topology. To bridge the connection between two nodes, we formally define a structure relation by encapsulating node attributes, between-node paths, and local topological structures together, which can make the inference conveniently deduced from one node to another node. For learning the inference process, we further introduce meta-optimization on structure relations from training nodes to validation nodes, such that the learnt graph inference capability can be better self-adapted to testing nodes. Comprehensive evaluations on four benchmark datasets (including Cora, Citeseer, Pubmed, and NELL) demonstrate the superiority of our proposed GIL when compared against state-of-the-art methods on the semi-supervised node classification task.