The design of stabilizing controllers for general nonlinear systems remains a challenging task due to their inherent complexities and nonconvexities. In this paper, we consider the problem of designing an asymptotically stable controller of a nonlinear dynamic system. We begin by framing the problem as an inverse optimal control problem, aiming to design a pair of cost functions that ensure asymptotic stability for the nonlinear model predictive control closed-loop system. By leveraging the relaxed dynamic programming inequality, a machine learning based algorithm is proposed to learn the cost functions. Finally, we demonstrate the effectiveness of the proposed method through illustrative examples.