We have measured the angle and polarization dependence of the absolute Raman scattering intensities of the 1340 and 1530 cm lines of Cu-phthalocyanine (CuPc) molecules adsorbed on the surfaces of an evaporated Ag film and a glass substrate with the incident laser line at 514.5 nm. The thickness of the CuPc layer was about a monolayer on the Ag substrate and five monolayers on the glass substrate. The scattering dipoles were found to lie parallel to the surface in both cases. The absolute molecular Raman cross sections were determined by including corrections for the effect of the substrate on the local incident field at the molecule and on the propagation of the scattered light. The Raman cross section of CuPc on the Ag substrate is about 150 times greater than that on the glass substrate. The relative enhancement of the Raman cross section on Ag is due to a resonant Raman effect arising from the electronic transitions that also cause absorption of the light at 514.5 nm.