News recommendation aims to display news articles to users based on their personal interest. Existing news recommendation methods rely on centralized storage of user behavior data for model training, which may lead to privacy concerns and risks due to the privacy-sensitive nature of user behaviors. In this paper, we propose a privacy-preserving method for news recommendation model training based on federated learning, where the user behavior data is locally stored on user devices. Our method can leverage the useful information in the behaviors of massive number users to train accurate news recommendation models and meanwhile remove the need of centralized storage of them. More specifically, on each user device we keep a local copy of the news recommendation model, and compute gradients of the local model based on the user behaviors in this device. The local gradients from a group of randomly selected users are uploaded to server, which are further aggregated to update the global model in the server. Since the model gradients may contain some implicit private information, we apply local differential privacy (LDP) to them before uploading for better privacy protection. The updated global model is then distributed to each user device for local model update. We repeat this process for multiple rounds. Extensive experiments on a real-world dataset show the effectiveness of our method in news recommendation model training with privacy protection.