An approach of contour error prediction based on long short-term memory neural network (LSTM) and Newton iteration and the contour error compensation by transforming the task coordinate system was proposed in order to address the problem that the accuracy of two-axis motion was affected by contour error. The feature contour and data were extracted from the control system of the two-axis motion platform, and the contour error was obtained by Newton’s method, which was employed as the training data of LSTM neural network. Then a more accurate prediction model of contour error was obtained. The predicted contour error was compensated to the reference contour through feedforward control by transforming the task coordinate system so as to improve the contour control performance. The random NRBUS curve was used to verify its generalization by comparing PID, ILC and neural network. The experimental results show that the proposed approach can effectively predict and control the contour error, and has good potential application value in the precision motion control.