Fourier transform infrared (FTIR) spectroscopy system uses He-Ne laser interference signal as a reference signal, but there is zero crossing sampling error. Based on the principle of light interference, a theoretical simulation model between FTIR spectroscopy sampling error and spectral ghost line position and intensity is established by Fourier transform. In order to reduce the sampling error, the cubic spline interpolation method is used to correct zero crossing error, and intensity of infrared optical interference signal is reconstructed by linear interpolation method. Results show that the model can be used as a theoretical basis for spectral error correction algorithm caused by sampling error. The cubic spline interpolation method can reduce the sampling error on reconstruction of He-Ne signal zero-crossing, and the error range is reduced by 93%. The linear interpolation method is applied to reconstruction of the infrared light intensity signal, which can improve the spectral signal-to-noise ratio, with an average increase of 5.7%.