Electronic mechanism of the surface enhanced Raman scattering (SERS) is investigated by an ab initio molecular orbital theory. The time-dependent Hartree-Fock method is used to calculate the polarizability of the surface-molecule interacting system. For representing the surface effect, we use small solid dusters Ag-2 Ag-10, K-2 Pd-2, and MgO. The present method succeeds in describing the enhancement of the Raman intensity for the adsorbed CO molecule. The maximum intensity of the Ag10CO system is calculated to be seven orders of magnitude larger than that of the free CO molecule. Furthermore, the wavelength dependence of the Raman intensity calculated by the Ag10CO system agrees with the experimental spectrum. The electronic mechanism of the SERS is due to the resonance transitions, in which the surface polarization and the surface-molecule interaction are very important. This mechanism explains the orientation- and distance-dependencies in the surface-adsorbate interacting systems.