In this paper a new class of higher order (F, ρ, σ)- type I functions over cones are defined for a multiobjective programming problem, which subsumes several known studied classes. A higher order Mond-Weir type dual program is formulated for a non-differentiable multiobjective programming problem over cones where the objective functions and the constraints contain support functions of compact convex sets in Rn. Weak and strong duality results are established by using the above defined functions.