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Collaborative Filtering (CF) is the main technology in recommendation systems. It requires more users' private information to predict personal preferences, so exists the risk of privacy disclosure. Differential Privacy (DP) is a powerful privacy-preserving approach, and it has been widely applied in CF-based recommendation system. However, a comprehensive summary of DP in CF-based recommendation system is lack although many privacy-preserving CF algorithms have been proposed. This paper reviews the existing research based on the principle of DP and the application of CF algorithms. We firstly introduce the theoretical basis and the mechanism employed by DP. Then, two types of CF-based recommendation algorithms with DP are summarized including memory-based and model-based algorithms. Moreover, the optimized CF algorithms with DP in specific application fields are illustrated.