Learning code representations has found many uses in software engineering, such as code classification, code search, code comment generation, and bug prediction. Although repre- sentations of code in tokens, syntax trees, dependency graphs, paths in trees, or the combinations of their variants have been proposed, existing learning techniques have a major limitation that these models are often trained on datasets labeled for specific downstream tasks, and the code representations may not be suitable for other tasks. Even though some techniques generate representations from unlabeled code, their effectiveness when applied to downstream tasks are far from satisfactory. To overcome the limitations, this paper proposes InferCode, which adapts the self-supervised learning idea from natural language processing to abstract syntax trees (ASTs) of code. The key novelty lies in the training of code representations by predicting subtrees automatically identified from the context of ASTs. With InferCode, subtrees in ASTs are treated as the labels for training the code representations without any human labeling effort or the overhead of expensive graph construction, and the trained representations are no longer tied to any specific downstream tasks or code units. We have trained an instance of InferCode using tree-based convolutional neural network (TBCNN) as the encoder on a large set of Java code. This pre-trained model can then be applied easily to downstream unsupervised tasks such as code clustering, code clone detection, cross-language code search, or be reused under a transfer learning scheme to continue training the model weights for supervised tasks such as code classification and method name prediction. In comparison with prior techniques applied to the same tasks, such as code2vec, code2seq, ASTNN, our pre-trained InferCode model achieves higher results in most of the tasks with a significant margin, including the task involving different programming languages. The implementation of InferCode and the trained embeddings are available at the anonymous link: https://github.com/ICSE21/infercode.