How to detect the high-quality community structures in location based social networks (LBSN) plays a significant role that helps to study and analyze this novel type of composite network comprehensively. However, most of existing community detection methods in social networks still cannot solve the problems of combining the correlations of multi-typed heterogeneous relations in LBSN. To address the issue, this paper proposes a co-clustering method for mining the users' community with multi-dimensional relationships, called Multi-BVD. Firstly, the objective function of clustering community is given to fuse multi-modal entities and their multi-dimensional relationships embedded in users' social network and geo-tagged location network. Then, in order to gain the minimum value of the given function, Lagrange multiplier method is applied to obtain the iterative upgrading rules of matrix variants so that the optimal results of users' communities can be determined by the way of decomposing block matrices. Simulation results show that the proposed Multi-BVD can find the community structures with geographical characteristics more effectively and accurately in location based social network. At the same time, the mined non-overlapping community has more cohesive structures in both social relationships and geographical tagged interests, which also can better embody the correlations of interests between users' communities and semantic geo-tagged clusters on locations.