In order to improve the machining accuracy of precision machine tools,two important error items of linear axis geometric error and thermal error were analyzed, a compound positioning error modeling method was proposed.The thermal error mechanism of the two-end fixed screw feed system was analyzed,the sine function error expression was established,bying using the finite element method, the screw surface temperature was extracted and substituted into the thermal error model as an input.The Chebyshev polynomials were used to establish a static geometric error prediction model.The two models were combined to obtain a composite positioning error model.The detection experiment on the linear axis of the precision machining center was carried out. After comparing the experimental value with the prediction model, it is found that the prediction accuracy is more than 85%, which verifies that the composite error model has high prediction accuracy and provides reference for linear axis positioning error compensation.