The WSGG-based narrow band model was employed to solve the radiative transfer equations along isothermal and non-isothermal paths through $CO_2-H_2O-N_2$ gas mixtures at 1 atm. When the WSGGM is applied for arbitrary gas mixtures by considering the multiplication property of transmissivity in overlapping bands, the number of gray gases is significantly increased. To reduce the computation time, three different regrouping methods for the gray gases are tested in obtaining the mean absorption coefficient for each gray gas group. Among them, the regrouping method by minimizing the regrouping error shows the best results. For the isothermal media, 10 gray gases show fairly good agreement with the results by statistical narrow band(SNB) model which are regarded as reference solutions. For non-isothermal media, 20 gray gases show good agreement with reference solutions.