Surface-enhanced Raman scattering (SERS) of graphene on a SiO(2)(300 nm)/Si substrate was investigated by depositing Au nanoparticles using thermal evaporation. This provided a maximum enhancement of 120 times for single-layer graphene at 633 nm excitation. SERS spectra and scan images of single-layer and few-layer graphene were acquired. Single-layer graphene provides much larger SERS enhancement compared to few-layer graphene, while in single-layer graphene the enhancement of the G band was larger than that of the 2D band. Furthermore, the D bands were identified in the SERS spectra; these bands were not observed in a normal Raman spectrum without Au deposition. Appearance of the D band is ascribed to the considerable SERS enhancement and not to an Au deposition-induced defect. Lastly, SERS enhancement of graphene on a transparent glass substrate was compared with that on the SiO(2)(300 nm)/Si substrate to exclude enhancement by multiple reflections between the Si substrate and deposited Au nanoparticles. The contribution of multiple reflections to total enhancement on the SiO(2)(300 nm)/Si substrate was 1.6 times out of average SERS enhancement factor, 71 times.