The applicability and usefulness of combustion in porous media is of much interest due to its competitive combustion efficiency and lower pollutants formation. In the previous works, the focus has been on the effects of combustion and heat transfer parameters such as excess air ratio, thermal power, solid conductivity, convective heat transfer coefficient, and radiation properties on centerline temperature and pollutant formations. A premixed combustion scheme and a fixed porous medium with constant geometrical parameters have been used in these works; therefore, the effects of porous material parameters have been less considered. In this research, the effects of geometrical parameters of porous medium, namely porosity and permeability, on centerline temperature distributions, peak flame temperature, flame structure, and gas mixture preheating have been investigated by numerical methods. To this, a two-dimensional axis-symmetric physical model of porous burner is considered. As the most typical porous burners, a two stage one which has preheating porous zone (PPZ) and combustion porous zone (CPZ) is studied. The continuity, momentum, energy, turbulence, and species transport equations are solved employing a one-step chemical reaction mechanism with an eddy-dissipation model for rate of reactions. The turbulence is modeled with two transport equations which are not considered in similar works. The combustion regime is assumed to be diffusion and combustion parameters are fixed in all cases. Porosity effects on the structure and temperature characteristic of the flame are probed in a wide range for PPZ and CPZ. Critical permeability is defined and permeability effects on flame characters in both of the preheating and combustion regions are studied thoroughly.