In the process of precision and ultra-precision machining, thermal error of CNC machine tool is a main error source that affects machining accuracy, and thermal error compensation technology is the most economical and effective method to reduce thermal error. For the prediction accuracy problem of thermal error compensation prediction model, a nonlinear combination prediction model was proposed. The single prediction model was screened by using the grey correlation method, and the selected single prediction models were combined linearly based on different optimization criteria. The generalized regression neural network was used to combine the linear combination model, and the nonlinear combination prediction model was obtained. The error prediction results show that compared with the typical BP neural network prediction model, the nonlinear combination prediction model has higher prediction accuracy, and the maximum error decreases from 4.78 μm to 0.7 μm.