The increasing reliance on ML models in high-stakes tasks has raised a major concern about fairness violations. Although there has been a surge of work that improves algorithmic fairness, most are under the assumption of an identical training and test distribution. In many real-world applications, however, such an assumption is often violated as previously trained fair models are often deployed in a different environment, and the fairness of such models has been observed to collapse. In this paper, we study how to transfer model fairness under distribution shifts, a widespread issue in practice. We conduct a fine-grained analysis of how the fair model is affected under different types of distribution shifts and find that domain shifts are more challenging than subpopulation shifts. Inspired by the success of self-training in transferring accuracy under domain shifts, we derive a sufficient condition for transferring group fairness. Guided by it, we propose a practical algorithm with fair consistency regularization as the key component. A synthetic dataset benchmark, which covers diverse types of distribution shifts, is deployed for experimental verification of the theoretical findings. Experiments on synthetic and real datasets, including image and tabular data, demonstrate that our approach effectively transfers fairness and accuracy under various types of distribution shifts.