Magnetism of interacting localized spins on triangular lattice has been of keen interest. We found a quantum spin liquid state in an organic Mott insulator with nearly triangular lattice by means of nuclear-magnetic-resonance experiments. The absence of long-range magnetic ordering was evidenced at low temperatures down to 30 mK in spite of an antiferromagnetic exchange interaction of 250 K between the neighboring spins. Realization of the spin liquid is attributable to the proximity of the present system to the Mott transition, consistent with the theoretical study of the triangular-lattice Hubbard model. Field-induced inhomogeneous spin state is argued in terms of the effect of disorder on the spin liquid.