Raman spectra of a single layer graphene sheet placed in different gold substrates were obtained and are discussed in the context of surface enhanced Raman scattering (SERS). The gold substrates were composed of a combination of a thermally deposited gold film and a close-packed gold nanosphere layer. The SERS effects were negligible when the excitation wavelength was 514 nm, while the Raman signals were enhanced 3-to 50-fold when the excitation wavelength was 633 nm. The large SERS enhancement accompanied a spectral distortion with appearance of several unidentifiable peaks, as well as enhancement of a broadened D peak. These phenomena are interpreted as the local field enhancement in the nanostructure of the gold substrates. The difference in the enhancement factors among the various gold substrates is explained with a model in which the spatial distribution and polarization of the local field and the orientation of the inserted graphene sheet are considered important.