Micro combustors can be used as the heat sources for micro power generation systems. Recently, we developed a micro Swiss-roll combustor for non-premixed fuel and air. In the current work, the impacts of channel height (H2 = 7.5, 7.0, 6.5, and 6.0 mm) on the combustion efficiency of CH4, and the surface radiation efficiency of this combustor were numerically investigated under constant flow rates of the fuel and air. The results showed that both combustion efficiency and radiation efficiency varied non-monotonically with the decrease of channel height. The optimal channel height was found to be 6.5 mm under which a highest combustion efficiency of 99.05 % and a highest radiation efficiency of 27.03 % were obtained. These variation rules were theoretically analyzed in terms of the heat recirculation effect on fresh reactants, the buoyancy effect on flame structure and chemical reaction, and the non-dimensional residence time of the reactants (DaL). It was unraveled that the combustor with H2 = 6.5 mm achieved a best heat recirculation effect. In addition, the buoyancy effect was weakened as the channel height was decreased, resulting in a more symmetric flame structure in the vertical direction and a more intense chemical reaction. Furthermore, when the channel height descended from H2 = 7.5 mm to 6.5 mm, the region of DaL > 1 was broadened due to the intensified reaction, but narrowed as the channel height was further reduced to 6.0 mm due to increased flow velocity. The combined actions of these factors led to non-monotonic variations of combustion efficiency and radiation efficiency. The discoveries of the present study provided a guideline for optimal design of such kind of micro Swiss-roll combustors.