The advancement of science and technology and the development of network environments have made social network multi-criteria group decision making (SN-MCGDM) an interesting research topic. A satisfaction-driven consensus model that can be applied to incomplete information under probabilistic linguistic trust in SN-MCGDM is presented. First, to model the trust relationships among group experts more flexibly and accurately, the concept of a probabilistic linguistic trust function is defined. Based on this concept, a t-norm-based probabilistic linguistic trust propagation operator and a path-weighted averaging operator are proposed to construct the complete trust relationships among group experts. Then, the incomplete evaluation information in the decision matrix is estimated based on the trust relationships. To identify inconsistent experts, a new consensus measure is provided. To achieve the individual aims as well as to retain the initial opinions of the experts to the greatest extent, identification rules based on satisfaction along with suggestion rules with local modifications are then proposed to help experts reach consensus. Finally, an example followed by comparative analyses is provided to verify the effectiveness of the proposed consensus-reaching model.