The Mott transition in the spin-frustrated organic conductor kappa-(ET)2Cu2(CN)3 with triangular lattice has been investigated by 1H NMR and resistivity measurements under pressure. Magnetic order is absent all through up to the critical pressure of Mott transition. The transition from the spin-liquid insulator to the strongly correlated Fermi liquid is identified with the temperature dependence of the spin-lattice relaxation rate and resistivity. We construct the pressure-temperature phase diagram, whose profile highlights the effect of spin frustration on the Mott transition.