In computing with words, it has been stressed that words mean different things for different people, which entails that decision makers (DMs) have personalized individual semantics (PISs) attached to linguistic expressions in linguistic group decision making (GDM). In particular, the PISs of DMs are not fixed, and they will be changing during the consensus building process, which indicates the necessary of continual PIS learning. Therefore, in this article, we propose a continual PIS-learning-based consensus approach in linguistic GDM. Specifically, a continual PIS learning model with the consistency-driven methodology is proposed to update the PISs taking into account all the linguistic preference data given by DMs during the consensus process. Then, the consensus measurement and feedback recommendation based on PIS are developed to detect the consensus process. Finally, numerical examples and simulation analysis are presented to illustrate and justify the use of the continual PIS-learning-based consensus approach.