Recovering a decentralized low-rank matrix from an incomplete set of its entries is one of great research interests. Privacy makes our issue difficult. In this paper, we propose a novel scheme that allows analysts to perform great aggregate analysis while guaranteeing meaningful protection of each individuals privacy. Differential privacy aims to ensure means to maximize the accuracy of queries from statistical databases while minimizing the probabilities of identifying its records. With adding Gaussian noise, we are able to achieve this goal. First, we present an algorithm for private matrix completion. Secondly, we provide theoretical results for required Gaussian noise. Finally, we compare the performance of the proposed algorithm with the state-of-the-art, while both achieves the same level of differential privacy.