Leveraging social network trust relationships among experts to reach consensus has become a popular topic in linguistic group decision making (GDM). However, in linguistic contexts, it is commonly accepted that words mean different things for different people, which indicates the necessity of modeling experts’ personalized individual semantics (PISs). Moreover, experts sometimes may show non-cooperative behaviors during the consensus reaching process (CRP) due to their own interests. As a result, this paper focuses on developing a consensus reaching algorithm with non-cooperative behavior management for PIS-based social network GDM problems. First, linguistic preference relations are transformed into fuzzy preference relations by the PIS model, and then social network analysis techniques are used to obtain experts’ weight vector. Afterwards, we propose a feedback adjustment mechanism to improve experts’ adjustment willingness in CPRs, in which the trust relationships and the PISs of experts are utilized to generate adjustment advice for experts. Furthermore, a non-cooperative behavior management mechanism which dynamically adjusts the trust degrees in social network is devised. Followed by this, a numerical example is provided to demonstrate the proposed algorithm. Finally, detailed simulation results are presented to analyze the influence of different parameters on CRPs and illustrate the validity of the proposed algorithm.