With the experimental data of positioning precision of highspeed precision CNC machine tool, a linear mathematical model of positioning error was established. Based on gray model and Cauchy problem formula, a nonlinear mathematical model was also established. The two models were evaluated by fuzzy comprehensive evaluation method to find the optimal prediction model. Compensated with a selected positioning error compensation model, the bound of the confidence interval 0.95 of positioning error is less than 3 μm. The results meet the design requirements of the machine tool.