The improvement of the detection limit of gas sensors has always been the focus of sensor research. Compared with the improvement of hardware, the improvement of the algorithm is still relatively less. In this study, a dual-channel methane gas sensor system based on mid-infrared LED light source was designed. We apply the wavelet denoising algorithm to the high-frequency noise suppression of the sensor system, which achieves a 36dB signal-to-noise ratio improvement over the traditional low-pass filter, making the detection limit of the sensing system reach the level below 3ppm. We give an estimation method for the detection limit of the sensing system. The detection limits estimated by this theory are basically the same as those obtained by the Allen deviation analysis in the conventional method. Implementing better algorithms to improve sensor SNR in software can reduce the demands of improving sensor SNR solely from hardware improvements.