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In this paper, based on genetic algorithm and steepest descent method, we proposed a sandwich-like new learning algorithm for neural network to identify chaotic systems. There are three stages in our new algorithm. The first stage searches, by steepest descent method, a set of more "nice" initial values for the learning of the weights in neural network. In the second stage, based on the initial values obtained from first stage, the genetic algorithm is used to make a global search of the weights which optimize the cost function of the output of neural network. In the third stage, for speeding up the convergent rate of the learning algorithm, the steepest descent method is used again to search the final optimal solution of weights. The chaotic system, logistic map, is considered for the simulation of our algorithm. Simulation results show that the algorithm proposed in this paper is more accurate and efficient than those of other methods.