In the measurement process of wavelength modulated laser absorption spectroscopy (WMS), the measurement system will inevitably be affected by circuit hardware noise, mechanical vibration noise, environmental noise and other factors. Taking the absorption spectrum of CH4 near 6 046.95 cm-1 as an example, the noise response characteristics of WMS technology are quantitatively studied by numerical simulation methods. The peak value changes of normalized second harmonic signals extracted by FFT filtering method under different signal-to-noise ratio are compared and analyzed. On this basis, the relationship between standard deviation and relative error of the second harmonic peak value change and the signal-to-noise ratio was modeled. Moreover, the approximate expression between the two and the signal-to-noise ratio was obtained, and the fitting R2 value are 0.999 57 and 0.993 52, respectively. Research results show that the method of data averaging cannot fundamentally eliminate the influence of noise on the accuracy of WMS measurement. The mathematical model established in this paper provides an idea for the correction of WMS measurement results under the influence of noise.