Aiming at the difficulty to analysis the regularity of CNC machine tools’ motion precision through mathematical model, the nonlinear prediction method based on chaotic phase space reconstruction theory was proposed. The optimum delay time was evaluated by the average mutual information method and the minimum embedding dimension calculated by false nearest neighbor method. The phase space reconstruction for one-dimensional time series of the motion accuracy was implemented. The topology isomorphic state space of the original system was obtained. According to the chaotic system’s inner orderliness and regularity, the phase points’ trajectory was employed to describe motion precision’s evolution regularity in phase space. The input vector was constituted by phase points’ multi-dimensional component, and the predictive value of the motion accuracy was used as output vector. The nonlinear prediction model of CNC machine tools’ motion precision was constructed based on RBF. In order to improve the prediction accuracy and generalization ability, the algorithm of quantum-behaved particle swarm optimization was proposed to select the parameters of RBF. Global optimum value of RBF network’s center, width and connection weights were obtained. Through the prediction model, the evolution trend of CNC machine tools’ motion precision was predicted. The experiments verified that the prediction model based on chaotic phase space reconstruction can trace the evolutionary trends and regularity of the precision properly. The maximum relative error of the precision was less than 6.67%.