Graph neural networks have pushed state-of-the-arts in graph classifications recently. Typically, these methods are studied within the context of supervised end-to-end training, which necessities copious task-specific labels. However, in real-world circumstances, labeled data could be limited, and there could be a massive corpus of unlabeled data, even from unknown classes as a complementary. Towards this end, we study the problem of semi-supervised universal graph classification, which not only identifies graph samples which do not belong to known classes, but also classifies the remaining samples into their respective classes. This problem is challenging due to a severe lack of labels and potential class shifts. In this paper, we propose a novel graph neural network framework named UGNN, which makes the best of unlabeled data from the subgraph perspective. To tackle class shifts, we estimate the certainty of unlabeled graphs using multiple subgraphs, which facilities the discovery of unlabeled data from unknown categories. Moreover, we construct semantic prototypes in the embedding space for both known and unknown categories and utilize posterior prototype assignments inferred from the Sinkhorn-Knopp algorithm to learn from abundant unlabeled graphs across different subgraph views. Extensive experiments on six datasets verify the effectiveness of UGNN in different settings.