In this paper, a new finite horizon iterative ADP algorithm is used to solve a class of nonlinear systems with state delay and control constraints problem and finite time ε-optimal control is obtained. First of all, a new performance index function is designed to deal with the control constraints, the discrete nonlinear systems HJB equation with state delay is presented. Second, the iterative process and mathematical proof of the convergence is illustrated for the proposed finite horizon ADP algorithm. Approximate optimal control is obtained by introducing an error bond ε. Two BP neural networks are developed to approximate control law function and performance index function in our ADP algorithm. Finally, comparing simulation cases are used to verify the effectiveness of the method proposed in this paper.