The purpose of this study is to propose a new prediction model T-DGM(2,n) and its application to predict the number of teachers for admission in Taiwan. T-DGM(2,n) is a prediction model based on Taylor approximation method in grey prediction to improve the predicted accuracy of DGM(2,n). The combined model can obtain the most optimal values of prediction by multi-times approximate calculation. In addition, researchers use the MATLAB software to build a MATLAB toolbox for this prediction model. The prediction results show that T-DGM(2,n) has good prediction performance. The results of this study will provide important information for educational administrators, and they can assist the government in developing future policies regarding educational management.