This paper addresses the issues of low accuracy and environmental susceptibility in existing methods for detecting mixed gas concentrations by proposing a method based on the improved TGWO-ELM (Teaching-Guided Firefly Algorithm optimized Extreme Learning Machine) algorithm, integrated with Tunable Diode Laser Absorption Spectroscopy (TDLAS) technology. The method leverages the extreme learning machine for gas concentration retrieval and employs the TGWO algorithm to mitigate stability issues stemming from the initial weights of the extreme learning machine and the random generation of offsets. The convergence factor′s attenuation formula is also improved to reduce algorithm training time. By simulating a single laser with the central wavelength of 1580nm, the large concentration difference experiment and the experiment of changing temperature condition are carried out for the mixed gas of CO and CO2, and the detection error can be stabilized at about 0.003%. Experiments show that the TGWO-ELM algorithm can effectively improve the detection accuracy, stability and response speed of mixed gas, and has high engineering application value.