To establish robust semantic correspondence between images covering different objects belonging to the same category, there are three important types of information including inter-image relationship, intra-image relationship and cycle consistency. Most existing methods only exploit one or two types of the above information and cannot make them enhance and complement each other. Different from existing methods, we propose a novel end-to-end Consistency Graph Modeling Network (CGMNet) for semantic correspondence by modeling inter-image relationship, intra-image relationship and cycle consistency jointly in a unified deep model. The proposed CGMNet enjoys several merits. First, to the best of our knowledge, this is the first work to jointly model the three kinds of information in a deep model for semantic correspondence. Second, our model has designed three effective modules including cross-graph module, intra-graph module and cycle consistency module, which can jointly learn more discriminative feature representations robust to local ambiguities and background clutter for semantic correspondence. Extensive experimental results show that our algorithm performs favorably against state-of-the-art methods on four challenging datasets including PF-PASCAL, PF-WILLOW, Caltech-101 and TSS.