Both entity and relation extraction can benefit from being performed jointly, allowing each task to correct the errors of the other. Most existing neural joint methods extract entities and relations separately and achieve joint learning  through parameter sharing, leading to a drawback that information between output entities and relations cannot be fully exploited. In this paper, we convert the joint task into a directed graph by designing a novel graph scheme and propose a transition-based approach to generate the directed graph incrementally, which can achieve joint learning through joint decoding. Our method can model underlying dependencies not only between entities and relations, but also between relations. Experiments on NewYork Times (NYT) corpora show that our approach outperforms the state-of-the-art methods.