Abstract: This paper introduces a new class of generalized invex function called d-ρηθ-univex function, and discusses the relationship among d-invex, d-univex, d-ρηθ-invex, and d-ρηθ-univex functions.Under d-ρηθ-univexity assumption, one type of multiobjective programming problem (P) is considered.The sufficient optimality conditions for the existence of the weak Pareto efficient solution of the problem (P) are first established.The results on the weak, strong and converse duality of Mond-Weir type duality, and the weak and strong duality assertions of the generalized Mond-Weir type duality of the problem (P) are then obtained.