Sum frequency generation vibrational spectroscopy （SFG-VS） is a robust technique for inter- facial investigation at molecular level. The performance of SFG-VS mostly depends on the spectral resolution of the SFG system. In this research, a simplified function was deduced to calculate the spectral resolution of picosecond SFG system and the lineshape of SFG spectra based on the Guassian shaped functions of IR beam and visible beam. The function indicates that the lineshpe of SFG spectra from nonresonant samples can be calculated by the Guassian widths of both IR beam and visible beam. And the Voigt lineshape of SFG spectra from vibrational resonant samples can be calculated by the Homogeneous broadening （Lorentzian width） and Inhomogeneous broadening （Guassian width） of vibrational modes, as well as the Guassian widths of both IR beam and visible beam. Such functions were also applied to verify the spectral resolution of the polarization-resolved and frequency-resolved picosecond SFG-VS system which was developed by our group recently. It is shown that the linewidths of IR beams that generated from current laser system are about 1.5 cm-1. The calculated spectral resolution of current picosecond IR scanning SFG-VS system is about 4.6 cm-1, which is consist with he spctral resolution shown in the spectra of cholesterol monolayer （3.5-5 cm-1）.
