A network-based method applied to collaborative filtering in recommender systems is introduced in this paper. Specifically, a novel mixed-membership stochastic block model with a conjugate prior from the exponential family is proposed for bipartite networks. The analytical expression of the model is derived, and a variational Bayesian algorithm that is computationally feasible for approximating the untractable posterior distributions is presented. Extensive simulations show that the proposed model provides more accurate inference than competing methods with the presence of outliers. The proposed model is also applied to a MovieLens dataset for a real data application.