Summary: In this paper, a new class of generalized \(K-(\Phi,\rho)\)-convex function is introduced, in which the sub linearity property of \(F\) as in literature is relaxed by imposing the convexity assumption on \(\Phi\) in its third argument with an example. This new class of generalized convex function is more generalized than the \((F,\alpha,\rho, d)\)-convex functions, \((C,\alpha,\rho, d)\)-convex functions and \(K-(F,\alpha,\rho, d)\) convex functions studied in literature. Also, a new model of higher order Wolfe type non-differentiable multi-objective symmetric dual programs is presented and the weak, strong and converse duality theorem under higher order \(K-(\Phi,\rho)\)-convex functions are established. Some special cases which generalizes our results is discussed.