Multi-hop machine reading comprehension (MRC) task aims to enable models to answer the compound question according to the bridging information. Existing methods that use graph neural networks to represent multiple granularities such as entities and sentences in documents update all nodes synchronously, ignoring the fact that multi-hop reasoning has a certain logical order across granular levels. In this paper, we introduce an Asynchronous Multi-grained Graph Network (AMGN) for multi-hop MRC. First, we construct a multigrained graph containing entity and sentence nodes. Particularly, we use independent parameters to represent relationship groups defined according to the level of granularity. Second, an asynchronous update mechanism based on multi-grained relationships is proposed to mimic human multi-hop reading logic. Besides, we present a question reformulation mechanism to update the latent representation of the compound question with updated graph nodes. We evaluate the proposed model on the HotpotQA dataset and achieve top competitive performance in distractor setting compared with other published models. Further analysis shows that the asynchronous update mechanism can effectively form interpretable reasoning chains at different granularity levels.