We present 13 C-NMR studies of the pressure-temperature phase diagram of the quasi-two-dimensional organic system EtMe 3 P͓Pd͑dmit͒ 2 ͔ 2 , which has a spin-gapped Mott insulating ground state at ambient pressure. As the system is pressurized, the spin-gapped insulating ground state survives until the insulator-metal Mott transition, just beyond which a superconducting state appears. This demonstrates that the superconducting phase borders the spin-gapped insulating phase. The phase diagram contrasts with those of the large majority of other correlated-electron superconductors in which the superconducting phase borders a magnetically ordered phase. This implies the possibility that the present superconductivity has an exotic origin and nature.