In the process of the ultra-precision grinding, the machining path of the aspherical is the result of motor coordination by several axes for the numerical control system. Since the motion of each axis have errors, there are big errors between the real positions and the theoretical positions, and the position error of the wheel infects the accuracy of the workpiece greatly. This paper analyses the position error property of the wheel and finds the machining approach path has nothing to do with the position error, just do with to the present machining point. In order to solve the problem, the method using the Neural Network optimized by the Genetic Algorithm to establish the position error model is introduced. A three-layer error back propagation (simplified as BP) Neural Network is used to establish the position error model, the position coordinates (x, z) of the program instruction is input layer, and the corroding measured error value ( Δx , Δz ) is output layer. Before training data sample, using the Genetic Algorithm to optimize the Neural Network to improve the predicting accuracy of the Neural Network, and reduce the training time. The emulation results indicate that using the Neural Network model optimized by the Genetic Algorithm can predict the position error in a high degree of accuracy, and at the same time, according to the predicting results, compensating the position error of the wheel is possible.