Distribution shift presents a significant challenge in machine learning, where models often underperform during the test stage when faced with a different distribution than the one they were trained on. In this paper, we focus on domain shifts, which occur when the model is applied to new domains that are different from the ones it was trained on, and propose a new approach called DG. Unlike previous approaches that aim to learn a single model that is domain invariant, DG leverages domain similarities based on domain metadata to learn domain-specific models. Concretely, DG learns a set of training-domain-specific functions during the training stage and reweights them based on domain relations during the test stage. These domain relations can be directly obtained and learned from domain metadata. Under mild assumptions, we theoretically prove that using domain relations to reweight training-domain-specific functions achieves stronger out-of-domain generalization compared to the conventional averaging approach. Empirically, we evaluate the effectiveness of DG using both toy and real-world datasets for tasks such as temperature regression, land use classification, and molecule-protein binding affinity prediction. Our results show that DG consistently outperforms state-of-the-art methods.