In order to establish the mathematical models of geometric errors of machine tools rapidly and precisely, one parametric modeling approach based on Chebyshev polynomials was proposed. Firstly, according to the measured data of basic geometric errors of machine tools, the displacement of the axis was converted to Chebyshev variable. Secondly, the values of Chebyshev polynomials with different orders were calculated with Chebyshev variable. Then, coefficients of Chebyshev basic functions were calculated by using multiple linear regression methods according to Chebyshev variable and Chebyshev values, and the model about Chebyshev basic functions was obtained. At last, the mathematical models of basic geometric errors were established by inputting the conversation of the displacement of the axis and Chebyshev variable. The modeling was simple and programming; and the high approximating accuracy of Chebyshev polynomials made models precise. The comprehensive mathematical models were established by inputting parametric models of geometric errors into geometric models of machine tools. Then, the geometric error fields of working zone for machine tools were obtained. Taking the MV—5A three-axis machine tool for an example, the parametric models of all geometric errors were inputted to geometric error model of this machine tool to obtain the comprehensive mathematical model of geometric errors. Then, geometric error fields of working zone of this machine tool were computed, which laid the foundation for machine design and the error compensation.