In this study the modified weighted sum of gray gases model (WSGGM) using the gray gas regrouping technique and the discrete ordinates interpolation method (DOIM) are applied to analyze the radiative transfer within an irregular 3-D enclosure filled with non-gray gas mixture of $CO_2$, $H_2O$ and $N_2$. The computer code developed in this study is successfully applied for solving the non-gray gas radiation within a 3-D rectangular enclosure and the gray gas radiation within an irregular 3-D enclosure by showing fairly good agreements with the existing results. In this paper the radiative transfer within an irregular 3-D enclosure filled with non-isothermal non-gray gases with uniform mixtures of $CO_2$, $H_2O$ and $N_2$ is studied to demonstrate the applicability of the modified sum of gray gases model for irregular systems and to examine the effect of the concentrations of $CO_2$ and $H_2O$ on the radiative transfer within modern combustors. Results show that the wall heat fluxes and the radiative heat source terms are increased as the concentrations of $CO_2$ and $H_2O$ are increased. Results also show that the radiative fluxes caused by the mixture gases with high concentrations $CO_2$ and $H_2O$ which can be observed in oxy-fuel combustion systems can reach up to nearly twice of those found in ordinary air-fuel combustion systems.