Summary: Hesitant normal fuzzy number synthesizes the distribution laws of normal fuzzy number and the uncertainty of hesitant fuzzy set which plays an important role in decision making problems. On some issues, the attributes of alternatives often have precedence relation. Aiming at this kind of problems, this paper puts forward hesitant normal fuzzy prioritized aggregation operator and hesitant normal fuzzy prioritized geometric aggregation operator, and investigates their properties. Based on that, we propose a reliable method for multiple-criteria group decision making problems. Finally, an illustrative example shows the effectiveness and feasibility of the proposed method.