Parts of geometric error coupled into space error is the main reason that affects machining accuracy of machine tools; therefore, how to determine the effect of geometric error to the machining accuracy and then assigning geometry precision of parts economically is a difficult problem in machine tool designing process. Therefore, based on multi-body system theory, a sensitivity analysis method of geometric error is put forward in this paper. Let’s take precision vertical machining center for an example. Firstly, an accuracy model of machining center is established based on multi-body system theory, and with 21 geometric errors obtained through experimental verification, key error sources affecting the machining accuracy are finally identified by sensitivity analysis. The example analysis shows that the proposed method can effectively identify the main geometric errors of parts that have great influence on volumetric error of machine tool, and thus provides important theoretical basis to improve the accuracy of machine tool economically.