Recently, lots of algorithms have been proposed for learning a fair classifier from centralized data. However, how to privately train a fair classifier on decentralized data has not been fully studied yet. In this work, we first propose a new theoretical framework, with which we analyze the value of federated learning in improving fairness. Our analysis reveals that federated learning can strictly boost model fairness compared with all non-federated algorithms. We then theoretically and empirically show that the performance tradeoff of FedAvg-based fair learning algorithms is strictly worse than that of a fair classifier trained on centralized data. To resolve this, we propose FedFB, a private fair learning algorithm on decentralized data with a modified FedAvg protocol. Our extensive experimental results show that FedFB significantly outperforms existing approaches, sometimes achieving a similar tradeoff as the one trained on centralized data.