The cold-start problem, faced when providing recommendations to newly joined users with no historical interaction record existing in the platform, is one of the most critical problems that negatively impact the performance of a recommendation system. Fortunately, cross-domain recommendation∼(CDR) is a promising approach for solving this problem, which can exploit the knowledge of these users from source domains to provide recommendations in the target domain. However, this method requires that the central server has the interaction behaviour data in both domains of all the users, which prevents users from participating due to privacy issues. In this work, we propose FedCDR, a federated learning based cross-domain recommendation system that effectively trains the recommendation model while keeping users' raw data and private user-specific parameters located on their own devices. Unlike existing CDR models, a personal module and a transfer module are designed to adapt to the extremely heterogeneous data on the participating devices. Specifically, the personal module extracts private user features for each user, while the transfer module is responsible for transferring the knowledge between the two domains. Moreover, in order to provide personalized recommendations with less storage and communication costs while effectively protecting privacy, we design a personalized update strategy for each client and a personalized aggregation strategy for the server. In addition, we conduct comprehensive experiments on the representative Amazon 5-cores datasets for three popular rating prediction tasks to evaluate the effectiveness of FedCDR. The results show that FedCDR outperforms the state-of-the-art methods in mean absolute error (MAE) and root mean squared error (RMSE). For example, in task Movie&Music, FedCDR can effectively improve the performance up to 65.83% and 55.45% on MAE and RMSE, respectively, when the new users are in the movie domain.