Next mobile app recommendation aims to recommend the next app that a user is most likely to use based on the user’s app usage behaviors, which is beneficial for improving user experience, app pre-loading, and system optimization. However, existing works ignore the complex dependencies between apps in the app usage sessions. In addition, they do not consider the dynamics of user interests over time. To address these concerns, we propose a novel model named dynamic usage graph network (DUGN) to recommend the next app that a user is most likely to use. To model the complex dependencies among apps explicitly, we adopt the dynamic graph structure to learn the dynamics of user interests. Firstly, we extract user interests in each app usage graph by using the hierarchical graph attention mechanism. Secondly, we capture user interests evolving over time, and generate the dynamic user embeddings by modeling the temporal dependencies among multiple app usage graphs. Finally, we obtain the current user interests in the current app usage graph, fuse multiple user interests and generate comprehensive user embeddings for next mobile app recommendation. We conduct experiments on real-world datasets. The results show that our model outperforms the state-of-art recommendation methods.