The choice of green suppliers involves a large amount of inaccurate, incomplete, and inconsistent information, and the single-valued triangular Neutrosophic number that is an extension of the single-valued Neutrosophic number can effectively handle such problems. Considering the advantages of the single-valued triangular Neutrosophic number, this paper proposes a new aggregate operator to solve the problem of multi-criteria decision making. The new aggregate operator takes into account the priority relationship and the interrelationship between the criteria. To make the new aggregate operator more flexible, this paper introduces the Dombi operations. This paper combines the Dombi operations with the prioritized average operator and the Bonferroni mean operator to propose the single-valued triangular Neutrosophic Dombi prioritized normalized Bonferroni mean (SVTNDPNBM) operator. Finally, the SVTNDPNBM operator is applied to the problem of the green supplier selection, which proves its feasibility and stability.