In this work, we present the first calculation of the resonance Raman scattering (RRS) spectrum of rhodamine 6G (R6G) which is a prototype molecule in surface-enhanced Raman scattering (SERS). The calculation is done using a recently developed time-dependent density functional theory (TDDFT) method, which uses a short-time approximation to evaluate the Raman scattering cross section. The normal Raman spectrum calculated with this method is in good agreement with experimental results. The calculated RRS spectrum shows qualitative agreement with SERS results at a wavelength that corresponds to excitation of the S-1 state, but there are significant differences with the measured RRS spectrum at wavelengths that correspond to excitation of the vibronic sideband of S-1. Although the agreement with the experiments is not perfect, the results provide insight into the RRS spectrum of R6G at wavelengths close to the absorption maximum where experiments are hindered due to strong fluorescence. The calculated resonance enhancements are found to be on the order of 10(5). This indicates that a surface enhancement factor of about 10(10) would be required in SERS in order to achieve single-molecule detection of R6G.