A three-point method based on sequential multilateration is applied to measuring the geometric error components (GECs) of three-axis machine tools (MTs). To meet the accuracy requirement of geometric error mapping, a sequential multilateration scheme is developed for high-accuracy point measurement by introducing four additional targets into the measuring system, and the uncertainty of point measurement is verified by simulation. Three independent targets fixed on the MT’s spindle assembly move along with each axis step by step and their coordinates at each step can be determined by the distance data acquired by laser tracker at all steps based on sequential multilateration. Then the volumetric errors of the three target points can be obtained by comparing the actual coordinates and the corresponding desired coordinates, and nine equations can be established by substituting volumetric errors into the error model of linear axis, so that the six GECs of each axis can be obtained by solving these equations. The three squareness errors can be determined by computing the angles between the average lines of the three axes which are achieved by linear curve fitting. Experiments are conducted to measure these 21 GECs, and the volumetric errors in the three-axis MT’s workspace, which are determined by these measured GECs based on the error model of three-axis MT, are compensated. Finally, the positioning errors of the MT with compensation and without compensation are evaluated by laser interferometer, respectively, the experimental results of which demonstrate that the positioning errors are significantly reduced by the error compensation.