Double-walled carbon nanotubes (DWNTs), synthesized by the catalytic decomposition of methane, were explored by resonance Raman spectroscopy using different energies for laser excitation. Based on the radial breathing mode frequencies, the indices of the two layers of a DWNT were approximately assigned, depending on the interlayer separation of the two coaxial layers of the DWNT, which ranged from 0.34 to 0.40 nm. From the tentatively assigned results, it was found that the two walls of the DWNT are not strongly selected by chirality and diameter. The results, however, suggest that, for the tubes that are resonant with the available laser excitation energies, most of the outer layers of the observed DWNTs in our samples are semiconducting, while the inner layers of the observed DWNTs are either semiconducting or metallic based on the assembled DWNTs. The characteristics of the G, D, and GЈ band of the DWNTs are discussed, and a double peak feature in the D and GЈ band, originating from the inner and outer layers of the DWNTs, is reported.