Characteristics of combustion in micro-channel heated by external heat source were examined. We chose quartz channel of inner diameter 2mm, being smaller than the quenching distance of Methane-air mixture. The effects of equivalence ratio and averaged mixture flow velocity on the stability were examined. In addition to the conventional flame, repetition of extinction and auto-ignition which we all "oscillatory combustion" was observed in wide equivalence ratio and smaller mixture velocity conditions. Mechanism of the phenomena was discussed by simple analysis.