In the present paper, DFT method at the B3LYP/6-31++G** (C, H, N, S)/LANL2DZ(Ag) level was used to optimize molecular configurations of p-aminothiophenol. Based on the optimized structure, the normal Raman scattering (NRS) spectrum of PATP and the surface-enhanced Raman scattering(SERS) spectrum of PATP adsorbed on Ag and Ag2 were both calculated, and were compared with the results of other literatures values. The calculation results indicated that a good conformity was found between the computed and experimental results. The results of PATP adsorbed on Ag2 were more approximate to the ever reported experimental data than those of PATP adsorbed on Ag. At the end, detailed analysis of the Raman spectrum and more comprehensive assignments of the vibration mode for p-aminothiophenol were studied by the software of GaussView. In comparison with SERS spectrum and NRS spectrum of PATP molecule, the authors observed the stretching vibration bands in the SERS spectrum at about 213 cm(-1), which is due to Ag-S stretching vibration mode. The work in this paper has greatly directive value in understanding and explaining some experiment phenomenon, and helps to study the mechanism of surface-enhanced Raman scattering of PATP.