By using two-loop renormalization group analysis, we explore the phase diagram with respect to the electron–phonon and Coulomb interaction strengths in the two (3,3)@(8,8) and (5,0)@(15,0) double-wall carbon nanotube systems (DWCNTs). Using estimation of the two types of coupling strengths from ab initio calculations, both systems are shown to scale to the superconducting fixed point as temperature decreases to zero. This is in contrast to the (3,3) and (5,0) single-wall carbon nanotubes, which scales to the Peierls-distorted semiconducting ground state. While the superconducting transition temperature can be quite low in the (3,3)@(8,8) system, the (5,0)@(15,0) promises observable superconducting behavior. Our result is in support of recent experimental observation of superconductivity in DWCNTs.