Preference relations have been widely used in group decision‐making (GDM) problems. Recently, a new kind of preference relations called fuzzy preference relations with self‐confidence (FPRs‐SC) has been introduced, which allow experts to express multiple self‐confidence levels when providing their preferences. This paper focuses on the analysis of additive consistency for FPRs‐SC and its application in GDM problems. To do that, some operational laws for FPRs‐SC are proposed. Subsequently, an additive consistency index that considers both the fuzzy preference values and self‐confidence is presented to measure the consistency level of an FPR‐SC. Moreover, an iterative algorithm that adjusts both the fuzzy preference values and self‐confidence levels is proposed to repair the inconsistency of FPRs‐SC. When an acceptable additive consistency level for FPRs‐SC is achieved, the collective FPR‐SC can be computed. We aggregate the individual FPRs‐SC using a self‐confidence indices‐based induced ordered weighted averaging operator. The inherent rule for aggregation is to give more importance to the most self‐confident experts. In addition, a self‐confidence score function for FPRs‐SC is designed to obtain the best alternative in GDM with FPRs‐SC. Finally, the feasibility and validity of the research are demonstrated with an illustrative example and some comparative analyses.