  We investigate electronic properties of the doped two-leg Hubbard ladder with
both the onsite and the nearest-neighbor Coulomb repulsions, by using the the
weak-coupling renormalization-group method. It is shown that, for strong
nearest-neighbor repulsions, the charge-density-wave state coexisting with the
p-density-wave state becomes dominant fluctuation where spins form intrachain
singlets. By increasing doping rate, we have also shown that the effects of the
nearest-neighbor repulsions are reduced and the system exhibits a quantum phase
transition into the d-wave-like (or rung-singlet) superconducting state. We
derive the effective fermion theory which describes the critical properties of
the transition point with the gapless excitation of magnon. The phase diagram
of the two-leg ladder compound, Sr_{14-x}Ca_xCu_{24}O_{41}, is discussed.
