Abstract: Gaps generally exist in lead screw pairs, gear transmission pairs and guide rail fitting pairs of the feed system of CNC mechanical equipment, and such gaps are the fundamental cause of positioning errors and contour errors. Systematic experiments are carried out on a certain three-axis vertical machining center, and a piecewise growth model of reverse error is established to quantitatively reveal the nonlinear transition law between gap values and positioning errors. The test results show that the composite compensation scheme proposed in this paper has the optimal performance. The axial reverse error is reduced from 42 μm to 4.8 μm, and the positioning accuracy is improved by 88.2%. All indicators meet the precision standards of precision-grade CNC machining centers.