Federated Learning (FL) is a novel privacy-protection distributed machine learning paradigm that guarantees user privacy and prevents the risk of data leakage due to the advantage of the client's local training. Researchers have struggled to design fair FL systems that ensure fairness of results. However, the interplay between fairness and privacy has been less studied. Increasing the fairness of FL systems can have an impact on user privacy, while an increase in user privacy can affect fairness. In this work, on the client side, we use fairness metrics, such as Demographic Parity (DemP), Equalized Odds (EOs), and Disparate Impact (DI), to construct the local fair model. To protect the privacy of the client model, we propose a privacy-protection fairness FL method. The results show that the accuracy of the fair model with privacy increases because privacy breaks the constraints of the fairness metrics. In our experiments, we conclude the relationship between privacy, fairness and utility, and there is a tradeoff between these.