Federated learning (FL) can achieve secure sharing of data, where all parties participate in model training locally and upload it to the server for aggregation. The data never leaves the parties involved, thus solving the problems of data privacy and data silos. However, FL faces issues such as high communication costs, imbalanced performance distribution among participants, and low privacy protection. To achieve a balance between model accuracy, communication cost, fairness, and privacy, this paper proposes a multi-objective optimization-based federated learning algorithm (M-FedAvg). The multi-objective optimization problem of maximizing the accuracy of the global model, minimizing the communication cost, minimizing the variance of the accuracy and minimizing the privacy budget is solved by NSGA-III. The experimental results show that the algorithm proposed can effectively reduce the communication cost of FL and achieve privacy protection for participants without affecting the accuracy of the global model.