The effect of radical quenching on the flame propagation and extinction limit in meso and microscale channels is investigated numerically using a three-step kinetic mechanism. The results showed that at low wall temperatures and large channel widths, the thermal quenching is a dominant mechanism for flame extinction. However, with the increase of the wall temperature and the reduction of the chain-branching temperature, radical quenching becomes an important or dominant mechanism in affecting flame speed, flame structure, and extinction limit. The results also show that the increase of flow velocity enhances the radical quenching effect. In addition, it is found that there are two different radical quenching regimes, the diffusion limited regime and the kinetic limited regime. It is shown that the decrease of radical Lewis number significantly reduces the flame speed and narrows the extinction limit. Moreover, the results also demonstrate that at high flow velocities, the radical quenching in microscale combustion can lead to a radical quenching induced extinction limit.