A new interval-valued intuitionistic fuzzy sets decision-making model based on the evidence theory is proposed. The attribute values of corresponding alternatives in this model are in the form of interval-valued intuitionistic fuzzy numbers (IVIFN). Firstly, IVIFN is converted into interval basic probability assignment (BPA). Then, the combination rule based on interval BPA is utilized to fuse different attributes. Finally, in order to make the final decision, the fused interval BPAs are transformed into classical BPA. In this way, multi-attribute information can be fused directly. The advantages of the proposed model lie in its simplicity, which better reflects the uncertainty of original data, and universality, which can be expanded to other field of interval-valued intuitionistic fuzzy sets easily. A numerical example is used to illustrate the effectiveness of the proposed method.