The weighted sum of gray gas model(WSGGM) is applied to arbitrary mixtures of CO$_2$ and H$_2$0 gases. To evaluate this model, the spectral and total intensities are obtained for two different problem types. One has uniform, parabolic and boundary layer type temperature profiles with uniform partial pressure, and the other has nonuniform partial pressure and temperature profile. The results obtained from the two different problem types show fairly good agreements with the results obtained by the statistical narrow band model(SNB model) which is regarded as the reference solutions. The WSGGM and its data base provided by this study can be used for analysis of radiative transfer by combustion gases with different thermal loadings and chemical compositions.