We present a quantu spin liquid state in a spin-1/2 honeycomb lattice with randomness in the exchange interaction. That is, we successfully introduce randomness into the organic radial-based complex and realize a random-singlet (RS) state. All magnetic and thermodynamic experimental results indicate the liquid-like behaviors, which are consistent with those expected in the RS state. These results demonstrate that the randomness or inhomogeneity in the actual systems stabilize the RS state and yield liquid-like behavior.