We recently developed a micro cavity-combustor which has a strong ability in flame stabilization and is promising to be used in micro power generation apparatus for MEMS and micro propulsion systems. In the present paper, the effect of wall thermal conductivity on the combustion efficiency of lean H-2/air flame was numerically investigated. It is shown that the decrease of combustion efficiency is due to flame-tip opening at high velocity. For the convenience of quantitative comparison, a "flame-splitting limit" was defined as the critical velocity when the combustion efficiency drops to 80%. It is very interesting to find that the flame-splitting limit exhibits a non-monotonic variation with the wall thermal conductivity. The analysis reveals that, for a larger thermal conductivity, the heat recirculation effect on the fresh mixture is better, which leads to higher flow velocity at the cavity exit; therefore, the flame front suffers stronger stretching effect and is splitted at a lower velocity. However, for a smaller thermal conductivity, the flow velocity in the central region of far downstream becomes faster, which results in stronger flame-stretching effect and smaller flame-splitting limit. In summary, a moderate thermal conductivity is advantageous to achieve high combustion efficiency. (C) 2015 Elsevier Ltd. All rights reserved.