The first example, as an organic compound, of the realization of superconductivity by a carrier-doping into a Mott-insulating state is presented. Although kappa- and kappa’-(BEDT-TTF)(2) Cu-2(CN)(3) have the same band structure, the former is a semiconductor, and the latter a metal at ambient pressure (AP). An extended Huckel band calculation and the spin susceptibility indicate that the kappa-salt is a Mott-insulator with an exactly half-filled band. On the other hand, the kappa’-salt shows an ESR signal of Cu2+ in addition to that of BEDT-TTF+. It is found that the metallic state and the superconductivity at AP of the kappa’-salt are realized by a carrier-doping by substituting Cu+ with Cu2+.