In order to decrease the influence of thermal errors on machining precision of machine tools and to improve the prediction accuracy of GMC(1,N) model,the cuckoo search(CS) algorithm was introduced into the grey system model GMC(1,N).The CS algorithm was proposed to optimize the GMC(1,N) generation coefficients.Then,the model based on CS-GMC(1,N) was established to predict the thermal error of CNC.By taking a small vertical milling center as an example,the thermal experiment was carried out.The analysis results of thermal error prediction performance indicate that the prediction accuracy of the CS-GMC(1,N) model is better than the PSO-GMC(1,N) model.The proposed modeling method provides reference for the thermal error modeling and subsequent thermal error compensation of CNC spindle.