To address the issue of instrument performance degradation of Fourier transform infrared (FTIR) spectrometers caused by different types of environmental signal noise, an adaptive filtering algorithm, which can update filtering parameters in real-time based on different environmental noise levels, is proposed in this work. The basic principle and implementation process of the algorithm are theoretically deduced, and the filtering effect under different filtering parameters is analyzed. Then, the proposed filtering algorithm is used to filter the measured spectral data, and the spectral signal-to-noise ratio (SNR) of different filtering methods is compared and analyzed. The results show that the SNRs of the adaptive filtering algorithm in 2100-2200 cm^-1 and 2500-2600 cm^-1 bands are 1.29 times and 1.13 times those of the traditional hardware filtering, respectively, indicating that the adaptive filtering algorithm proposed can effectively improve SNR of FTIR spectrum and the performance index of FTIR instrument.