Federated learning enables multiple parties to collaboratively learn a model without exchanging their local data. Currently, federated averaging (FedAvg) is the most widely used federated learning algorithm. However, FedAvg or its variants have obvious shortcomings. It can only be used to learn differentiable models and needs many communication rounds to converge. In this paper, we propose a novel federated learning algorithm FedKT that needs only a single communication round (i.e., round-optimal). With applying the knowledge transfer approach, our algorithm can be applied to any classification model. Moreover, we develop the differentially private versions of FedKT and theoretically analyze the privacy loss. The experiments show that our method can achieve close or better accuracy compared with the other state-of-the-art federated learning algorithms. While the size of training data can influence the machine learning model quality a lot, the data are often dispersed over different parties in reality. Due to regulations on data privacy, the data cannot be centralized to a single party for training. To address these issues, federated learning (Kairouz et al., 2019; Li et al., 2019a;b; Yang et al., 2019) enables multiple parties to collaboratively learn a model without exchanging their local data. It has become a hot research topic and shown promising results in the real world (Bonawitz et al., 2019; Hard et al., 2018; Li et al., 2020a; Peng et al., 2020). Currently, federated averaging (FedAvg) (McMahan et al., 2016) is a widely used federated learning algorithm. Its training is an iterative process with four steps in each iteration. First, the server sends the global model to the selected parties. Second, each of the selected parties updates its model with their local data.