This paper presents a new method for multicriteria fuzzy decision making based on the ranking interval-valued intuitionistic fuzzy values, where interval-valued intuitionistic fuzzy values are used to represent evaluating values of the decision-maker with respect to alternatives. We propose a new method for ranking interval-valued intuitionistic fuzzy values. Based on the proposed fuzzy ranking method of interval-valued intuitionistic fuzzy values, we propose a new method for multicriteria fuzzy decision making. We also use an example to illustrate the multicriteria fuzzy decision making process of the proposed method. The proposed method provides us with a useful way for dealing with multicriteria fuzzy decision making problems based on ranking interval-valued intuitionistic fuzzy values.