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Point-of-Interest (POI) recommendation has been extensively studied and successfully applied in industry recently. However, most existing approaches build centralized models on the basis of collecting users' data. Both private data and models are held by the recommender, which causes serious privacy concerns. In this paper, we propose a novel Privacy preserving POI Recommendation (PriRec) framework. First, to protect data privacy, users' private data (features and actions) are kept on their own side, e.g., Cellphone or Pad. Meanwhile, the public data need to be accessed by all the users are kept by the recommender to reduce the storage costs of users' devices. Those public data include: (1) static data only related to the status of POI, such as POI categories, and (2) dynamic data depend on user-POI actions such as visited counts. The dynamic data could be sensitive, and we develop local differential privacy techniques to release such data to public with privacy guarantees. Second, PriRec follows the representations of Factorization Machine (FM) that consists of linear model and the feature interaction model. To protect the model privacy, the linear models are saved on users' side, and we propose a secure decentralized gradient descent protocol for users to learn it collaboratively. The feature interaction model is kept by the recommender since there is no privacy risk, and we adopt secure aggregation strategy in federated learning paradigm to learn it. To this end, PriRec keeps users' private raw data and models in users' own hands, and protects user privacy to a large extent. We apply PriRec in real-world datasets, and comprehensive experiments demonstrate that, compared with FM, PriRec achieves comparable or even better recommendation accuracy.