The single-molecule surface-enhanced Raman scattering (SERS) spectra of Rhodamine 6G (R6G) in an aqueous environment under non-resonance conditions are studied. Series of spectra are recorded in timemapping mode, and intensity fluctuations of SERS signals and spectral diffusion are observed. The correlations between the presence frequency of SERS spectra and number of hot spots as well as the quantity of molecules in scattering volume are examined thoroughly. The results indicate that only molecules located at hot spots produce good signal-to-noise ratio Raman spectra and the origin of fluctuating SERS signals are mainly ascribed to the movement of hot spots.