In order to solve the problem that information could be easily lost in the phase space constructed by the unit precision time series with finite length or containing noises, the method of predicting numerical control machine’s motion precision was put forward based on multivariate chaotic time series. Firstly, multiple characteristic quantity of motion precision were extracted from CNC machine tool. Delay time and embedding dimension of the multiple motion precision time series were worked out by the C-C algorithm. The low-dimensional sequences were mapped to high-dimensional space to establish a multi-precision state space by phase reconstruction of multivariate time series. The phase space established was the same topological isomorphism with the original system. The state space points’ track was described motion precision’s evolution in multivariate phase space. Then the principal component analysis was used to reduce dimensions of high dimensional phase space and remove redundant information. Finally, the state vector of the phase space was taken as a multi-dimensional input. The predicting model of wavelet neural network could be trained by the information constructed to achieve the motion precision prediction. The experiments results showed that the proposed method could well analyze the changing regulation of NC machine tools motion precision and the mean square error of prediction model was 0.0095. Compared with the way of prediction by the unit chaotic time series, it had better predictive effects, and its adaptability and practicality were stronger.