To suppress sensor noise with unknown statistical properties, a novel self-adaptive direct laser absorption spectroscopy (SA-DLAS) technique was proposed by incorporating a recursive, least square (RLS) self-adaptive denoising (SAD) algorithm and a 3291 nm interband cascade laser (ICL) for methane (CH) detection. Background noise was suppressed by introducing an electrical-domain noise-channel and an expectation-known-based RLS SAD algorithm. Numerical simulations and measurements were carried out to validate the function of the SA-DLAS technique by imposing low-frequency, high-frequency, White-Gaussian and hybrid noise on the ICL scan signal. Sensor calibration, stability test and dynamic response measurement were performed for the SA-DLAS sensor using standard or diluted CH samples. With the intrinsic sensor noise considered only, an Allan deviation of ~43.9 ppbv with a ~6 s averaging time was obtained and it was further decreased to 6.3 ppbv with a ~240 s averaging time, through the use of self-adaptive filtering (SAF). The reported SA-DLAS technique shows enhanced sensitivity compared to a DLAS sensor using a traditional sensing architecture and filtering method. Indoor and outdoor atmospheric CH measurements were conducted to validate the normal operation of the reported SA-DLAS technique.