Diffraction in the Fourier-transform infrared spectrometer based on step mirrors was analyzed in the present paper, and the influence of diffraction on the spectrum reconstruction with different width of step mirrors, wavelengths and distance was also discussed. It is shown that the influence of diffraction is low when the distance is less than 10 cm and the width of mirror is more than 0.5 mm. Also, a method to reduce the noises in spectrum reconstuction is discussed in this paper. The results could be used in the design of the spectrometer and the data processing in the next step.