Abstract: An approximate dynamic programming (ADP) approach was proposed for a class of unknown nonlinear zero-sum game. A model based on a recurrent neural network (RNN) was used to approximate the unknown system dynamics. A novel adjustable term related to the modeling error was added to the RNN model, which guaranteed the modeling error convergent to zero. Then, an ADP approach was given to solve the optimal performance index and the optimal control pair under the saddle point of the zero-sum game existence or not. Simulation results demonstrated the effectiveness of the proposed control scheme.