Unsteady simulations were performed to investigate the flame structure and the dynamic behavior of a premixed flame exposed to the wall heat loss. A 3-step global reaction mechanism was adopted in this study. Simulations were performed for two tube combustors with inner diameters($d_i$) of 1mm and 4mm. The material of tube combustor was assumed to be a Silicon Nitride($Si_{3}N_4$). The heat loss from the outer tube wall was controlled by adjusting the amount of convective and radiative heat loss. A conical premixed flame could be stabilized inside a tube of $d_i=4mm$. The flame stability inside a tube of $d_i=4mm$ combustor was not much sensitive to the amount of heat loss. In case of a tube of $d_i=1mm$, an oscillating flame was observed in very low heat loss condition and a flame could not be sustained in realistic heat loss condition.