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Matrix factorization is one of the most commonly used technologies in recommendation system. With the promotion of recommendation system in e-commerce shopping, online video and other aspects, distributed recommendation system has been widely promoted, and the privacy problem of multi-source data becomes more and more important. Based on Federated learning technology, this paper proposes a shared matrix factorization scheme called SharedMF. Firstly, a distributed recommendation system is built, and then secret sharing technology is used to protect the privacy of local data. Experimental results show that compared with the existing homomorphic encryption methods, our method can have faster execution speed without privacy disclosure, and can better adapt to recommendation scenarios with large amount of data.