This paper proposes a new method that it uses the neural network to construct the solution of the Hamiltion-Jacobi inequality (HJ), and it carries on the optimization of the neural network weight using the genetic algorithm. This method causes the Lyapunov function to satisfy the HJ, avoides solving the HJ parital differential inequality, and overcomes the difficulty which the HJ parital differential inequality analysis. Beside this, it proposes a design method of a nonlinear state feedback L2-gain disturbance rejection controller based on HJ, and introduces general structure of L2-gain disturbance rejection controller in the form of neural network. The simulation demonstrates the design of controller is feasible and the closed-loop system ensures a finite gain between the disturbance and the output.