We present a self-consistent theory of the interplay between the d-density wave (DDW) and superconductivity on the basis of the fluctuation-exchange (FLEX) approximation for the twodimensional (2D) Hubbard model with the nearest-neighbor hopping t and on-site Coulomb repulsion U. In order to stabilize the DDW state with respect to phase separation at lower dopings a small nearestneighbor Coulomb repulsion V is included within the Hartree-Fock approximation. The competition between the DDW and superconductivity can generically result in the appearance of a new superconducting state, which has the p-pairing order parameter. We solve the gap equations for competing DDW, BCS, and p-pairing order parameters with d-wave symmetry, together with calculating the FLEX interaction self-consistently, and calculating the corresponding three transition temperatures T n , T c , and T c n as a function of hole doping. The calculated phase diagram has a quantum critical point (QCP) separating a pure BCS superconducting state at large dopings d4d 0 from a coexisting DDW and p-pairing state at lower dopings dod 0 . Remarkable is the much higher value of the T c n for the p-pairing superconductivity as compared with the pure BCS superconductivity.