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Massive real-world data are network-structured, such as semantic web, social network, relationship between proteins, etc. Modeling a network is an effective way for better understanding the properties of a network, while avoiding the complexity of the full description. This paper proposes a novel hierarchical Bayesian model for relational data, which is an extension of Mixed Membership Stochastic Block model. Unlike previous work assumes edges to be of atomic, our model recognizes that each edge is composed of multiple elementary relationships and the weight on this edge is a includes all the weights of these elementary relationships. This allows our model to incorporate more information about the network and increases its ability of uncertainty tolerance. A fast inference based on variational inference is offered. Empirical results on a synthetic data and three real-world data sets demonstrate the effectiveness and the robustness of our method.