The hyper-Raman and surface enhanced hyper-Raman spectra of benzene, pyridine and pyrazine were calculated by ab initio method. The results of theoretical calculation and experiments were compared. The molecular dipole moments, the polarizabilities, and hyper-polarizabilities were calculated by using density functional theory (DFT) methods based on Gaussian 98. The dipole moment and polarizability derivatives were provided automatically by Gaussian 98, but the hyper-polarizatibily derivatives were determined by a finite difference method. To make sure the accuracy of this method, it was used to calculate the infrared (IR) and Raman spectra, and the results are in agreement with the analytical results provided by Gaussian 98. The methods for calculating spectra of IR, Raman, surface enhanced Raman scattering (SERS), hyper-Raman scattering (HRS), and surface enhanced hyper-Paman scattering (SEHRS) of molecules were built up based on ab initio and the finite difference method.