Although Raman spectra reveal, as a signature of double-walled carbon nanotubes (DWCNTs), two radial breathing mode (RBM) lines associated with the inner and outer tubes, the specification of their nature as metallic or semiconducting remains a topic for debate. Investigating the spectral range of the RBM lines, we present a new procedure of the indexing of the semiconducting or metallic nature of the inner and outer shell that forms the DWCNT. The procedure exploits the difference between the intensities of recorded anti-Stokes Raman spectrum and the anti-Stokes spectrum calculated by applying the Boltzmann formulae to the recorded Stokes spectrum. The results indicate that the two spectra do not coincide with what should happen in a normal Raman process, namely, that there are RBM lines of the same intensity in both spectra, as well as RBM lines of higher intensity that are observed in the calculated spectrum. This discrepancy results from the surface-enhanced Raman scattering mechanism that operates differently on metallic or semiconducting nanotubes. In this context, the analysis of the RBM spectrum can reveal pairs of lines associated with the inner/outer shell structure of DWCNT, and when the intensities between the recorded and calculated spectra coincide, the nanotube is metallic; otherwise, the nanotube is semiconducting.