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In the federated learning setting, multiple clients jointly train a model under the coordination of the central server, while the training data is kept on the client to ensure privacy. Normally, inconsistent distribution of data across different devices in a federated network and limited communication bandwidth between end devices impose both statistical heterogeneity and expensive communication as major challenges for federated learning. This paper proposes an algorithm to achieve more fairness and accuracy in federated learning (FedFa). It introduces an optimization scheme that employs a double momentum gradient, thereby accelerating the convergence rate of the model. An appropriate weight selection algorithm that combines the information quantity of training accuracy and training frequency to measure the weights is proposed. This procedure assists in addressing the issue of unfairness in federated learning due to preferences for certain clients. Our results show that the proposed FedFa algorithm outperforms the baseline algorithm in terms of accuracy and fairness.