Document-level relation extraction aims to model the reasoning information over multiple sentences of a document and capture complex dependency interactions between inter-sentence entities. However, modeling reasoning information effectively in the document remains a challenging task. In this paper, we propose a Collaborative Local-Global Reasoning Network (CLGR-Net) for the Document-Level Relation Extraction model to effectively predict such relations by integrating rich local and global information from the multi-granularity graph. Specifically, CLGR-Net first constructs a mention-level graph and a concept-level graph. The former aggregates complex local interactions underlying the same entities, the latter captures long-distance global interaction among different entities. Finally, it creates an entity-level graph, the nodes and edges of the entity graph are aggregated by Relational Graph Convolutional Networks (R-GCN) and enriched by probability Knowledge Graphs (KGs), based on which we design a novel hybrid reasoning mechanism to collaborate relevant global and local information for entities. In this way, our model can effectively model reasoning information from these three graphs. The mention-level graph and concept-level graph are used as auxiliary information for the entity-level graph in the form of independent heterogeneous graphs. Our CLGR-Net model achieves more competitive performance than state-of-the-art on three widely used benchmarks.