Most practical decision-making problems commonly contain several alternatives evaluated by more than one decision maker (DM) according to the built criteria system. It is known as multi-criteria group decision making problems. The decision-making results should be based on highly similar individual opinions to derive the most suitable choice. Nevertheless, the divergence of individual judgments is usually significant due to various subjective and objective reasons. In this case, some DMs need to modify their judgments to derive final results, the consensus adjustment in group decision making. Like supply chain management, the centralized consensus process can minimize individual adjustments under the set consensus condition. Based on the hypothesis of rational humans that individuals always pursue maximum benefits, this paper proposes an iterative consensus process in a centralized environment. According to non-consensus adjustments, the iterative procedure contains non-transferable and transferable two parts. When the non-transferable consensus adjustment procedure is completed, the transferable consensus adjustment procedure is activated using an asymmetrical Nash bargaining game allocation mechanism. Additionally, a case study is provided to demonstrate the efficaciousness and practicality of the new method. Meanwhile, sensitivity and comparison analyses are done.