An electrical-domain self-adaptive mid-infrared absorption spectroscopy for methane detection based on an interband cascade laser was demonstrated. By adding noise into the laser drive signal, denoising and sensing performances were evaluated for the technique. Experiments were made to study the effects of noise level/type on sensor stability, characterized by Allan deviation. High- and low-frequency noise levels have the same functional variation trend on Allan deviation, which differs from white Gaussian noise. Within a noise level range of 0-125 mV for low- and high-frequency noise and 0-62.5 mV for white Gaussian noise in the mercury-cadmium-telluride detector's output (with a pure signal amplitude of ~300 mV), the sensor stability using self-adaptive denoising was enhanced by a factor of 1.05-20, 1.32-6.25, and 1.15-3.33 times compared to that using no filtering, for the three kinds of noise, respectively. The reported self-adaptive methane sensor system shows enhanced stability compared to the direct laser absorption spectroscopy sensor using traditional sensing architecture and classic filtering method. The sensor was further evaluated through outdoor atmospheric methane measurements using such technique. A second-order self-adaptive direct laser absorption spectroscopy technique was also proposed for noise suppression in both optical and electrical domain as an outlook of the concept of this paper.