The frequency of an external-cavity diode laser has been stabilized to absorption line of methane at wavelengths around 1.6 μm by employing the wavelength modulation technique and the digitized controller. The frequency fluctuation of the stabilized laser is held within 5.6 MHz and better than 160 MHz of the free-running laser. The root of Allan variance of error signals reaches a minimum of 1.66×10 -11 when averaging time is 64 s, well within the precision needed for application. And various limiting factors are analyzed. It is found that the stability is mostly limited by the noise of photodetector and frequency modulation in the experiment. Several methods of improved stability are also presented here. Such a treatment can provide a guidance of any experiment of frequency stabilization. The primary application of this stabilized laser is to provide a frequency reference for remote sensing of the concentration of methane.