In the present study, combustion phenomenon and heat transfer in a 3-D rectangular porous radiant burner (PRB) are numerically studied. Methane- air mixture with detailed chemical kinetics is considered to model the combustion process inside the porous matrix. Assuming the non-local thermal equilibrium between solid and gas phases, separate energy equations are considered for two phases. Porous medium is assumed as a gray medium that can absorb, scatter, and emit thermal radiation, where the gas phase is considered to be transparent. The governing equations including gas and porous energy equations, the chemical species transport equation and the radiative transfer equation are simultaneously and numerically solved. Discrete ordinates method is used to solve the radiative transfer equation in order to calculate the radiative term in the solid energy equation. The simulation results include temperature fields for the gas and solid phase, species mass fraction distributions, and radiative heat flux profiles along the burner. Finally, the effect of different parameters such as optical thickness, scattering albedo, excess air ratio (EAR) and porosity on the performance of burner are explored.