As a novel and efficient surface analysis technique, graphene-enhanced Raman scattering (GERS) has attracted increasing research attention in recent years. In particular, chemically doped graphene exhibits improved GERS effects when compared with pristine graphene for certain dyes, and it can be used to efficiently detect trace amounts of molecules. However, the GERS mechanism remains an open question. We present a comprehensive study on the GERS effect of pristine graphene and nitrogen-doped graphene. By controlling nitrogen doping, the Fermi level (EF) of graphene shifts, and if this shift aligns with the lowest unoccupied molecular orbital (LUMO) of a molecule, charge transfer is enhanced, thus significantly amplifying the molecule's vibrational Raman modes. We confirmed these findings using different organic fluorescent molecules: rhodamine B, crystal violet, and methylene blue. The Raman signals from these dye molecules can be detected even for concentrations as low as 10(-11) M, thus providing outstanding molecular sensing capabilities. To explain our results, these nitrogen-doped graphene-molecule systems were modeled using dispersion-corrected density functional theory. Furthermore, we demonstrated that it is possible to determine the gaps between the highest occupied and the lowest unoccupied molecular orbitals (HOMO-LUMO) of different molecules when different laser excitations are used. Our simulated Raman spectra of the molecules also suggest that the measured Raman shifts come from the dyes that have an extra electron. This work demonstrates that nitrogen-doped graphene has enormous potential as a substrate when detecting low concentrations of molecules and could also allow for an effective identification of their HOMO-LUMO gaps.