Collaborative filtering (CF) recommendation algorithms are well-known for their outstanding recommendation performances, but previous researches showed that they could cause privacy leakage for users due to k-nearest neighboring (KNN) attacks. Recently, the notion of differential privacy (DP) has been applied to privacy preservation for collaborative filtering recommendation algorithms. However, as far as we know, existing differentially private CF recommendation schemes degraded the recommendation performance (such as recall and precision) to an unacceptable level. In this paper, in order to address the performance degradation problem, we propose a differentially private user-based collaborative filtering recommendation scheme based on k-means clustering (KDPCF). Specifically, to improve the recommendation performance, we first cluster the dataset into categories by k-means clustering and appropriately adjust the size of the target category to which the target user belongs, so that only users in the well-sized target category can be used for recommendations. Then we efficiently select a set of neighbors from the target category at one time by employing only one exponential mechanism instead of the composition of multiple ones, and base on the neighbor set to recommend. We theoretically prove that our scheme achieves differential privacy. Empirically, we use the MovieLens dataset to evaluate our recommendation system. The experimental results demonstrate a significant performance gain compared to existing schemes.