The development of social media has revolutionized the way people communicate, share information and make decisions, but it also provides an ideal platform for publishing and spreading rumors. Existing rumor detection methods focus on finding clues from text content, user profiles, and propagation patterns. However, the local semantic relation and global structural information in the message propagation graph have not been well utilized by previous works. In this paper, we present a novel global-local attention network (GLAN) for rumor detection, which jointly encodes the local semantic and global structural information. We first generate a better integrated representation for each source tweet by fusing the semantic information of related retweets with the attention mechanism. Then, we model the global relationships among all source tweets, retweets, and users as a heterogeneous graph to capture the rich structural information for rumor detection. We conduct experiments on three real-world datasets, and the results demonstrate that GLAN significantly outperforms the state-of-the-art models in both rumor detection and early detection scenarios.