The minimum amount that can be detected and quantitatively analyzed by Fourier infrared spectrometer depends on the signal-to-noise ratio of the measured gas spectrum. In order to use Fourier transform infrared absorption spectroscopy to measure CO₂, CO, CH₄, N₂O and other greenhouse gases, the signal-to-noise ratio and instrument detection limit of the mixed gas are studied. We propose a method to calculate the gas detection limit of the instrument through the HITRAN simulation spectrum. In addition, we build an experimental platform to verify the accuracy of the detection limit approximation based on the HITRAN simulation spectrum calculation, which serves as the actual measurement detection limit of the instrument, and we also analyze the reasons why there appears the error between the existing experimental platform and optimization scheme and their deficiencies as well.