To discuss the optimality and duality conditions for a class of generalized invariant convex multi-objective programming problems. A new class of generalized convex functions, namely generalized (G-V, ρ) invariant convex functions, is introduced with the help of Clarke subdifferential; the corresponding indifferentiable multi-objective programming problems and the G-Mond-Weir dual problems are studied. The optimality conditions for the indifferentiable multi-objective programming problems and the weak duality, strong duality and strict inverse duality for the G-Mond-Weir duality problem are obtained.The study on generalized (G-V, ρ) invariant convex functions enriches the content of multi-objective programmings, which is of great significance for the subsequent research in related fields.