This paper aims to offer a new group decision-making (GDM) method based on interval-valued intuitionistic fuzzy preference relations (IVIFPRs). To furnish this goal, a new additive consistency definition of IVIFPRs is first proposed. Then, a programming model is built to check the additive consistency of IVIFPRs. For incomplete IVIFPRs, two programming models are constructed, which aim at maximizing the consistency and minimizing the uncertainty of missing information. To achieve the minimum total adjustment, a goal programming model is established to repair inconsistent IVIFPRs. Considering the consensus, a programming model for improving the consensus degree is established, which permits different IVIFVs to have different adjustments and makes individual IVIFPRs have the smallest total adjustment to remain more original information. Based on these results, a consistency- and consensus-based GDM method is proposed. At length, a practical example for screening new majors of a private college in China is offered to illustrate the feasibility and efficiency of proposed method.