We report the results of SQUID and torque magnetometry of an organic spin-$1/2$ triangular-lattice $\kappa -{\mathrm{H}}_3(\text{Cat-EDT-TTF}{)}_2$. Despite antiferromagnetic exchange coupling at 80–100 K, we observed no sign of antiferromagnetic order down to 50 mK owing to spin frustration on the triangular lattice. In addition, we found nearly temperature-independent susceptibility below 3 K associated with Pauli paramagnetism. These observations suggest the development of gapless quantum spin liquid as the ground state. On the basis of a comparative discussion, we point out that the gapless quantum spin liquid states in organic systems share a possible mechanism, namely the formation of a band with a Fermi surface possibly attributed to spinons.