When Fourier-transform infrared spectroscopy is used to on-line detection of high-temperature gas in an industrial furnace, the noise formed by turbulence will affect the spectral signal-to-noise ratio and the accuracy of concentration inversion. This paper introduces a new data processing method for infrared interference signal-spectrum conversion. Different from the traditional data processing method for Fourier transform spectra, this method takes the zero optical path difference as the reference to align the interference signals and averages multiple scanning interference signals. It adopts the complex window function and spectral data convolution to reduce the spectral aliasing caused by spectral sidelobes. This data processing algorithm can mitigate the effect of turbulent noise on the gas concentration inversion, improve the inversion accuracy, reduce the amount of system calculation, and increase the spectral data rate. Taking the passive measurement experiment of carbon monoxide with superimposed turbulence as an example, this paper analyzes the spectral signal-to-noise ratio, spectral correlation, and concentration inversion results using different data processing methods. The results show that the proposed signal data processing method is better than traditional data processing methods in the online detection of turbulent noise. The spectrum obtained by the new data processing method is more precise (with better spectral correlation), and the concentration of gas inversion is also more accurate. In addition, it can decrease the amount of system computation and shorten the time of the system’s online measurement. This is essential for the accuracy of online gas concentration monitoring.