Document-level relation extraction aims to extract relations between entities in a document. In contrast to sentence-level relation extraction, it deals with longer texts and more complex entity interactions, which requires reasoning over multiple sentences with rich reasoning skills. Most current researches construct a document-level graph first, and then focus on the overall graph structure or the paths between the target entity pair in the graph. In this paper, we propose a novel subgraph reasoning (SGR) framework for document-level relation extraction. SGR combines the advantages of both graph-based models and path-based models, integrating various paths between the target entity pair into a much simpler subgraph structure to perform relational reasoning. Moreover, the paths generated by our designed heuristic strategy explicitly model the requisite reasoning skills and roughly cover the supporting sentences for each relation instance. Experimental results on DocRED show that SGR outperforms existing models, and further analyses demonstrate that our method is both effective and explainable. Our code is available at https://github.com/Crysta1ovo/SGR.