  Recently, Matsukawa et al. have discovered a new superconductor
Pr_2Ba_4Cu_7O_15-delta in which metallic CuO double chains are responsible for
the superconductivity. To investigate the superconductivity, we employ the d-p
double chain model where the tight-binding parameters are determined so as to
fit the LDA band structure. On the basis of the Tomonaga-Luttinger liquid
theory, we obtain the phase diagram including the superconducting phase in the
weak coupling limit. We also calculate the Luttinger liquid parameter K_rho as
a function of the electron density $n$ by using the Hartree-Fock approximation.
With increasing $n$ from quarter filling, K_rho increases, and then exceeds 1/2
when the superconducting correlation becomes most dominant. K_rho has a maximum
at an optimal density between quarter- and half-filling. These results are
consistent with the experimental observation.
