Abstract: In this research, the aim of the study is to present a method to solve a class of inverse optimal value problem with linear constraints by using a nonlinear gradient neural network. Firstly, based on optimal theory, solving the inverse optimal value problem is changed as solving a nonlinear bilevel program problem equivalently. Then a nonlinear gradient neural network model for solving the nonlinear bilevel programming is presented. By employing Lyapunov function approach, the proposed neural network is analyzed to be globally Lyapunov stable and capable of generating approximal optimal solution to the nonlinear bilevel programming problem. Finally, numerical examples are provided to verify the feasibility and the efficiency of the proposed method in this study.