In order to solve the problem of large sample demand and low computational efficiency in the current sensitivity analysis method, a global sensitivity analysis method based on polynomial chaos expansion was proposed. Firstly, a complete spatial error model was established based on the screw theory by taking the AC type double turntable five-axis CNC machine tool as the research object. Secondly, the polynomial chaos expansion model of machine tool geometric error was constructed. The orthogonal matching pursuit was used to sparse the model, and the Sobol sensitivity index based on this method was given. Furthermore, the geometric errors of five-axis CNC machine tools were analyzed. he approximate probability distribution of 41 errors are measured and counted, and the key geometric errors affecting he pose error components in each direction are analyzed. Compared with Monte Carlo simulation and Latin hypercube ampling, the correctness of the polynomial chaos expansion method is verified. Under the premise of not reducing the calculation accuracy, the sample size is reduced from 1×10⁵ to 1×10³, the calculation time is reduced by 96.8% and 98.1% respectively, and the calculation efficiency is significantly improved.