The paper develops a new intuitionistic fuzzy (IF) programming method to solve group decision making (GDM) problems with interval-valued fuzzy preference relations (IVFPRs). An IF programming problem is formulated to derive the priority weights of alternatives in the context of additive consistent IVFPR. In this problem, the additive consistent conditions are viewed as the IF constraints. Considering decision makers’ (DMs’) risk attitudes, three approaches, including the optimistic, pessimistic and neutral approaches, are proposed to solve the constructed IF programming problem. Subsequently, a new consensus index is defined to measure the similarity between DMs according to their individual IVFPRs. Thereby, DMs’ weights are objectively determined using the consensus index. Combining DMs’ weights with the IF program, a corresponding IF programming method is proposed for GDM with IVFPRs. An example of E-Commerce platform selection is analyzed to illustrate the feasibility and effectiveness of the proposed method. Finally, the IF programming method is further extended to the multiplicative consistent IVFPR.