Graph clustering has a long-standing problem in that it is difficult to identify all the groups of vertices that are cohesively connected along their internal edges but only sparsely connected along their external edges. Apart from structural information in social networks, the quality of the location-information clustering has been improved by identifying clusters in the graph that are closely connected and spatially compact. However, in real-world scenarios, the location information of some users may be unavailable for privacy reasons, which renders existing solutions ineffective. In this paper, we investigate the clustering problem of privacy-preserving social networks, and propose an algorithm that uses a prediction-and-clustering approach. First, the location of each invisible user is predicted with a probability distribution. Then, each user is iteratively assigned to different clusters. The experimental results verify the effectiveness and efficiency of our method, and our proposed algorithm exhibits high scalability on large social networks.