Fairness in machine learning has attracted increasing attention in recent years. The fairness methods improving algorithmic fairness for in-distribution data may not perform well under distribution shifts. In this paper, we first theoretically demonstrate the inherent connection between distribution shift, data perturbation, and model weight perturbation.Subsequently, we analyze the sufficient conditions to guarantee fairness (i.e., low demographic parity) for the target dataset, including fairness for the source dataset, and low prediction difference between the source and target datasets for each sensitive attribute group. Motivated by these sufficient conditions, we propose robust fairness regularization (RFR) by considering the worst case within the model weight perturbation ball for each sensitive attribute group. We evaluate the effectiveness of our proposed RFR algorithm on synthetic and real distribution shifts across various datasets. Experimental results demonstrate that RFR achieves better fairness-accuracy trade-off performance compared with several baselines. The source code is available at \url{https://github.com/zhimengj0326/RFR_NeurIPS23}.