Federated Learning （FL） is a machine learning setting that can protect data privacy， however， the problems of high communication cost and client heterogeneity hinder the large?scale implementation of federated learning. To solve these two problems， a federated learning algorithm for communication cost optimization was proposed. First， the generative models from the clients were received and simulated data were generated by the server. Then， the simulated data were used by the server to train the global model and send it to the clients， and the final models were obtained by the clients through fine?tuning the global model. In the proposed algorithm only one round of communication between clients and the server was needed， and the fine?tuning of the client models was used to solve the problem of client heterogeneity. When the number of clients is 20， experiments were carried out on MNIST and CIFAR?10 dataset. The results show that the proposed algorithm can reduce the amount of communication data to 1/10 of that of Federated Averaging （FedAvg） algorithm on the MNIST dataset， and can reduce the amount of communication data to 1/100 of that of Federated Averaging （FedAvg） algorithm on the CIFAR-10 dataset with the premise of ensuring accuracy.