Abstract: In this paper, a decision making method considering additive consistency and group consensus is proposed to solve group decision making problems with linguistic intuitive fuzzy preference relations. For the method, local iteration algorithm is utilized to improve linguistic intuitionistic fuzzy preference relation consistency and strengthen the consensus reached process and keep the original reasonable information as much as possible. First of all, a transformation formula is proposed to convert an intuitive fuzzy weight vector into a additive consistent linguistic intuitive fuzzy preference relation and a goal programming model is designed to derive its normalized intuitive fuzzy weights. Secondly, for linguistic intuitive fuzzy preference relations with inconsistent addition, a local iteration method is proposed to improve the consistency. Then, an enhanced consensus reaching procedure is developed to help the group of decision makers find a solution which is accepted by most members in the group. In order to make better use of the decision-making method in this paper, a global decision algorithm is presented. Finally, an example is given to illustrate that the method is reasonable and effective.