This study presents the idea of using a porous media burner to improve the oxy-methane combustion reaction rate and broaden the stability limit. Numerical studies on the premixed combustion of CH4/O2/CO2 in a two-layer porous medium burner using a two-dimensional symmetrical volume-average model with the skeleton mechanism based on OpenFOAM. The combustion characteristics of burners with variable cross-sectional (VC) and straight cylindrical (SC) structures were compared, including stable range, temperature field, thermal cycle efficiency, and CO emissions. It is confirmed that the cross-sectional structure is effective for broadening the stable range, and the broadening rate is more than 4 times. As more heat is lost from the outlet due to the increased cross-section, the solid-phase temperature of VC is lower than that of SC. As a result, the flame temperature of VC will be about 200 K lower than that of SC under the condition of insulated walls. It also leads to a reduction of about 2% in thermal cycle efficiency compared with SC. Meanwhile, it is shown that the VC structure slightly increases CO emissions at low thermal power but is smaller than that of SC at high power. When the wall heat loss of the burner is considered, the VC structure is still effective for improving the stable range. In addition, the VC structure slightly affects flame tilt and temperature uniformity at the burner outlet when the thermal power is large. It is confirmed that the VC structure is effective for increasing the power adjustment range and reducing pollutant emissions at high power.