With the development of information and network technology, group decision making problems based on social network have attracted the attention of more and more researchers. This paper focuses on a consensus adjustment process and an alternative selection approach for the group decision making problems with fuzzy complementary judgement matrices under the social network environment. Firstly, we build a trust relationship among decision makers by fusing the information from three aspects: social relation among decision makers, the decision maker’ status, and his/her knowledge ability. Then a consensus index is proposed to minimize consensus compensation between elements as far as possible, a consensus model based on the trust relationship is established, and the feasibility of the model is proved theoretically. Finally, the eigenvector centrality of the trust matrix is used to calculate the weights of experts, which is incorporated into aggregating the individual preference values and ranking alternatives. The effectiveness of the proposed method is further verified by a numerical example.