In the mobile Internet era, the recommender system has become an irreplaceable tool to help users discover useful items, and thus alleviating the information overload problem. Recent deep neural network (DNN)-based recommender system research have made significant progress in improving prediction accuracy, which is largely attributed to the access to a large amount of users' personal data collected from users' devices and then centrally stored in the cloud server. However, as there are rising concerns around the globe on user privacy leakage in the online platform, the public is becoming anxious by such abuse of user privacy. Therefore, it is urgent and beneficial to develop a recommender system that can achieve both high prediction accuracy and high degree of user privacy protection. To this end, we propose a DNN-based recommendation model called PrivRec running on the decentralized federated learning (FL) environment, which ensures that a user's data never leaves his/her during the course of model training. On the other hand, to better embrace the data heterogeneity commonly existing in FL, we innovatively introduce a first-order meta-learning method that enables fast in-device personalization with only few data points. Furthermore, to defense from potential malicious participant that poses serious security threat to other users, we develop a user-level differentially private DP-PrivRec model so that it is unable to determine whether a particular user is present or not solely based on the trained model. Finally, we conduct extensive experiments on two large-scale datasets in a simulated FL environment, and the results validate the superiority of our proposed PrivRec and DP-PrivRec.