In order to reduce the time of neural network self-learning, it proposes an algorithm which combines genetic algorithm (GA) and neural network prediction together. Genetic algorithm is used to search the optimal solution globally, and the data generated by GA during evolutionary process are used to train a predictive network. The predictive network establishes a mapping between parameters of operant networks and system response (fitness). When the genetic algorithm converges to adjacent domains of optimal solution, the predictive network guides it to converge to the optimum solution depending on its approximation for arbitrary function. The predictive network solves local vibration problem of GA and accelerates the speed of self-learning. The proposed algorithm is applied to design a speed controller of asynchronous motor drive system and a lot of simulation results validate the feasibility of the proposed algorithm.