To improve the prediction accuracy and robustness of the spindle thermal error compensation model of computer numerical control （CNC） machine tools， this study investigates the application of the principal component algorithm to the thermal error modeling of CNC machine tools. First， a selection algorithm of the temperature sensitive point and thermal error modeling algorithm based on principal component algorithm are proposed. Second， a three-axis vertical machining center is used to measure the spindle thermal error over an entire year. Thereafter， the principal component regression （PCR） model of the spindle thermal error is established based on the experimental data obtained. Then， the prediction accuracy and robustness of the PCR model are compared with those of the multivariate linear regression， back propagation （BP） neural network， and ridge regression models. The experimental results show that the PCR model has the highest prediction accuracy （6.8 μm） and robustness （2.4 μm）. Finally， the developed PCR model is used to predict the thermal errors of machine spindles that operate according to the speed spectrum. In this case， the model exhibits a prediction accuracy and robustness of 6.12 μm and 3.43 μm， respectively. Finally， the PCR model is embedded into the thermal error compensation controller for performing thermal error compensation experiments to verify the effectiveness of the proposed modeling algorithm.