The Raman spectroscopic properties of Pt-CO molecule have been investigated based on the electronic state 1 sigma + determined by the HF and B3LYP methods. The result shows that the calculated stretching vibrational frequencies of the Pt-C and C-O bonds depend on the method and the basis sets used. It indicates that it is important to adopt an appropriate method to describe pi-donation and pi-back-donation bond. The result of the differential Raman scattering cross section for the stretching vibrations of the Pt-C and C-O bond shows that the latter is significantly larger value compared to the former.