The effects of pressure, flow velocity and mixture composition on extinction limits of premixed methane/air flames in a mesoscale channel (2mm) with a temperature gradient were studied both experimentally and numerically at low pressure conditions (0.2-0.05atm). An external heat source was employed to form a steady temperature gradient along the channel for simulating the state of the heat recirculation. At low pressure conditions, combustion in a small-scale channel can be simulated since flame becomes thicker with the decrease of pressure. Both experimental and numerical results showed that maximum upper blow-off limits were found to be at the fuel-leaner side under low pressure conditions. That is, the flammable regions under low pressure conditions showed tendencies asymmetric to the stoichiometric mixture ratio, while the conventional flammable region at atmospheric pressure is symmetric to it. Furthermore, computational results implied the existence of a lower extinction limit of stable flame although heat loss was compensated for by the external heater.