Fourier transform spectroscopy with bandpass sampling (BPS-FTS) increases the interferogram sampling step and reduces sampling frequency, thereby reducing system implementation difficulty. However, this technology has only been introduced in principle and lacks analysis of the actual system error. In this paper, we present a theoretical analysis of the optical system diffraction effect, derive the bandpass spectrum bandwidth and interferogram sampling step under the influence of the diffraction effect, and conduct modeling and a simulation analysis with and without the diffraction effect. Through simulation, we found that when the diffraction effect was considered, the relative deviation of the recovered spectrum from the input spectrum was 1.30%, and the spectral similarity was 0.9669. However, without considering the diffraction effect, the relative deviation of the recovered spectrum from the input spectrum was 6.23%, and the spectral similarity was only −0.0056. The simulation results demonstrate that the diffraction effect has a significant influence on BPS-FTS interferogram sampling and recovery spectra. The results of this study have reference significance for their technical realization of BPS-FTS.