News recommendation is critical for personalized news access. Most existing news recommendation methods rely on centralized storage of users' historical news click behavior data, which may lead to privacy concerns and hazards. Federated Learning is a privacy-preserving framework for multiple clients to collaboratively train models without sharing their private data. However, the computation and communication cost of directly learning many existing news recommendation models in a federated way are unacceptable for user clients. In this paper, we propose an efficient federated learning framework for privacy-preserving news recommendation. Instead of training and communicating the whole model, we decompose the news recommendation model into a large news model maintained in the server and a light-weight user model shared on both server and clients, where news representations and user model are communicated between server and clients. More specifically, the clients request the user model and news representations from the server, and send their locally computed gradients to the server for aggregation. The server updates its global user model with the aggregated gradients, and further updates its news model to infer updated news representations. Since the local gradients may contain private information, we propose a secure aggregation method to aggregate gradients in a privacy-preserving way. Experiments on two real-world datasets show that our method can reduce the computation and communication cost on clients while keep promising model performance.