Double-wall carbon nanotubes (DWCNTs) were synthesized by pyrolyzing C2H2 on the sulfur-promoted floating iron catalyst. Similar to that of SWCNTs, Raman spectra of DWCNTs display two "fingerprint" features of the radial breathing mode (RBM) at the lower frequency range and the splitting tangential mode (TM). However, RBM frequencies of DWCNTs take a wider range and display much richer peaks than those of SWCNTs. The possible match of the inner tubes and the outer tubes according to the RBM bands was assigned, and different chirality types were discussed according to the diameter and chirality dependence of resonant Raman vibration. By changing experimental conditions, we can tunably grow different DWCNTs with various diameter distributions.