The narrow band-averaged transmissivity of $CO_2-H_2O$ mixtures is expressed by multiplying the transmissivities of $CO_2;and;H_2O$. Applying the multiplication property of narrow band transmissivities for gas mixtures of $CO_2-H_2O$ of the narrow band based WSGGM (weighted sum of gray gases model), the number of gray gases, required for accurate representation of the absorption characteristics by using the narrow band based WSGGM, is significantly increased. To reduce the computational loads by reducing the number of gray gases, we propose a gray gas regrouping process where the gray gases used for .the WSGGM are regrouped into a specified number of groups according to the magnitudes of absorption coefficients. To evaluate the proposed WSGGM for gas mixtures, the radiative transfer problems through 3-dimensional gas media are considered. The radiative source terms and the radiative heat fluxes obtained by using the proposed method are fairly well compared to previous results obtained by using the SNB model and other models. The regrouping technique results in an excellent computational efficiency with minor loss of accuracy.