Recent works have made great progress in semantic segmentation by exploiting contextual information in a local or global manner with dilated convolutions, pyramid pooling or self-attention mechanism. However, few works have focused on harvesting boundary information to improve the segmentation performance. In order to enhance the feature similarity within the object and keep discrimination from other objects, we propose a boundary-aware graph convolution (BGC) module to propagate features within the object. The graph reasoning is performed among pixels of the same object apart from the boundary pixels. Based on the proposed BGC module, we further introduce the Boundary-aware Graph Convolution Network(BGCNet), which consists of two main components including a basic segmentation network and the BGC module, forming a coarse-to-fine paradigm. Specifically, the BGC module takes the coarse segmentation feature map as node features and boundary prediction to guide graph construction. After graph convolution, the reasoned feature and the input feature are fused together to get the refined feature, producing the refined segmentation result. We conduct extensive experiments on three popular semantic segmentation benchmarks including Cityscapes, PASCAL VOC 2012 and COCO Stuff, and achieve state-of-the-art performance on all three benchmarks.