We present a novel Bipartite Graph Reasoning GAN (BiGraphGAN) for the challenging person image generation task. The proposed graph generator mainly consists of two novel blocks that aim to model the pose-to-pose and pose-to-image relations, respectively. Specifically, the proposed Bipartite Graph Reasoning (BGR) block aims to reason the crossing long-range relations between the source pose and the target pose in a bipartite graph, which mitigates some challenges caused by pose deformation. Moreover, we propose a new Interaction-and-Aggregation (IA) block to effectively update and enhance the feature representation capability of both person's shape and appearance in an interactive way. Experiments on two challenging and public datasets, i.e., Market-1501 and DeepFashion, show the effectiveness of the proposed BiGraphGAN in terms of objective quantitative scores and subjective visual realness. The source code and trained models are available at https://github.com/Ha0Tang/BiGraphGAN.