Surface-stabilized combustion burners is a promising combustion technique that has been studied for more than a decade. However, in the design stage of these burners is hard to determine if under certain operating conditions the burner would operate adequately. In this paper, we performed a numerical approach to predict the flame stability in a surface-stabilized combustion burner. Here we considered a numerical approach that includes simultaneous solution of mass and energy balance for both, the gas and solid phase, as well as a proper estimation of thermo-chemical and thermo-physical properties. The numerical model was validated against experimental data reported in previous studies. These data involve results with natural gas and the blending of natural gas with three high hydrogen content synthetic gases in equimolar proportions. We evaluated three synthetic gases with high hydrogen contents ranging from 60% H2 to 75% H2. The data also involve thermal power from 300 to 500 kW/m2. The results indicate that the numerical approach described in this work predicts very well the flame stability and temperature profile within the porous media. Therefore, it can be used to study surface-stabilized combustion burners. © Published under licence by IOP Publishing Ltd.