Grounding referring expressions is a fundamental yet challenging task facilitating human-machine communication in the physical world. It locates the target object in an image on the basis of the comprehension of the relationships between referring natural language expressions and the image. A feasible solution for grounding referring expressions not only needs to extract all the necessary information (i.e. objects and the relationships among them) in both the image and referring expressions, but also compute and represent multimodal contexts from the extracted information. Unfortunately, existing work on grounding referring expressions cannot extract multi-order relationships from the referring expressions accurately and the contexts they obtain have discrepancies with the contexts described by referring expressions. In this paper, we propose a Cross-Modal Relationship Extractor (CMRE) to adaptively highlight objects and relationships, that have connections with a given expression, with a cross-modal attention mechanism, and represent the extracted information as a language-guided visual relation graph. In addition, we propose a Gated Graph Convolutional Network (GGCN) to compute multimodal semantic contexts by fusing information from different modes and propagating multimodal information in the structured relation graph. Experiments on various common benchmark datasets show that our Cross-Modal Relationship Inference Network, which consists of CMRE and GGCN, outperforms all existing state-of-the-art methods.