We studied the modulation of Raman scattering intensities of molecules on graphene by tuning the graphene Fermi level with electrical field effect (EFE). A series of metal phthalocyanine (M-Pc) molecules (M = Mn, Fe, Co, Ni, Cu, Zn), which have different molecular energy levels, were used as probe molecules. The Raman intensities of all these M-Pc molecules become weaker when the graphene Fermi level is up-shifted by applying a positive gate voltage, while they become stronger when the graphene Fermi level is down-shifted by applying a negative gate voltage. However, this Raman intensity modulation only occurs when applying the gate voltage with a fast sweep rate, while it is nearly absent when applying the gate voltage with a slow sweep rate, which is likely due to the arising of the hysteresis effect in the graphene EFE. In addition, the Raman modulation ability for M-Pc molecules with smaller energy gaps is larger than that with larger energy gaps due to the difference in the energy alignment between graphene and these M-Pc molecules. Furthermore, this modulation shows the greatest one on single-layer graphene and mainly comes from the first layer of molecules which are in direct contact with graphene. The Raman modulation of molecules in GERS with the EFE suggests that the Raman enhancement for GERS occurs through a chemical enhancement mechanism.