A quantum spin-liquid state, an exotic state of matter, appears when strong quantum fluctuations enhanced by competing exchange interactions suppress a magnetically ordered state. Generally, when an ordered state is continuously suppressed to 0 K by an external parameter, a quantum phase transition occurs. It exhibits critical scaling behaviour, characterized only by a few basic properties such as dimensions and symmetry. Here we report the low-temperature magnetic torque measurements in an organic triangular-lattice antiferromagnet, kappa-(BEDT-TTF)(2)Cu-2(CN)(3), where BEDT-TTF stands for bis(ethylenedithio)-tetrathiafulvalene. It is found that the magnetic susceptibilities derived from the torque data exhibit a universal critical scaling, indicating the quantum critical point at zero magnetic field, and the critical exponents, gamma = 0.83(6) and nu z = 1.0(1). These exponents greatly constrain the theoretical models for the quantum spin liquid, and at present, there is no theory to explain the values, to the best of our knowledge.