Domain adaptation, which aims to transfer knowledge between domains, has been well studied in many areas such as image classification and object detection. However, for multi-modal tasks, conventional approaches rely on large-scale pre-training. But due to the difficulty of acquiring multi-modal data, large-scale pre-training is often impractical. Therefore, domain adaptation, which can efficiently utilize the knowledge from different datasets (domains), is crucial for multi-modal tasks. In this paper, we focus on the Referring Expression Grounding (REG) task, which is to localize an image region described by a natural language expression. Specifically, we propose a novel approach to effectively transfer multi-modal knowledge through a specially relation-tailored approach for the REG problem. Our approach tackles the multi-modal domain adaptation problem by simultaneously enriching inter-domain relations and transferring relations between domains. Experiments show that our proposed approach significantly improves the transferability of multi-modal domains and enhances adaptation performance in the REG problem.