  We propose that when the Fermi level lies within a wide band and also lies
close to but not within a coexisting narrow band, high $T_c$ superconductivity
may take place due to the large number of interband pair scattering channels
and the small renormalization of the quasiparticles. We show using fluctuation
exchange method that this mechanism works for the Hubbard model on a ladder
lattice with diagonal hoppings. From this viewpoint, we give a possible
explanation for the low $T_c$ for the actual hole doped ladder compound, and
further predict a higher $T_c$ for the case of electron doping.
