In recent years, with the development of the Internet, the data on the network presents an outbreak trend. Big data mining aims at obtaining useful information through data processing, such as clustering, clarifying and so on. Clustering is an important branch of big data mining and it is popular because of its simplicity. A new trend for clients who lack of storage and computational resources is to outsource the data and clustering task to the public cloud platforms. However, as datasets used for clustering may contain some sensitive information (e.g., identity information, health information), simply outsourcing them to the cloud platforms can't protect the privacy. So clients tend to encrypt their databases before uploading to the cloud for clustering. In this paper, we focus on privacy protection and efficiency promotion with respect to k-means clustering, and we propose a new privacy-preserving multi-user outsourced k-means clustering algorithm which is based on locality sensitive hashing (LSH). In this algorithm, we use a Paillier cryptosystem encrypting databases, and combine LSH to prune off some unnecessary computations during the clustering. That is, we don't need to compute the Euclidean distances between each data record and each clustering center. Finally, the theoretical and experimental results show that our algorithm is more efficient than most existing privacy-preserving k-means clustering.