In this paper, we determine the electronic transport properties of Au–C20–Au molecular system under finite bias voltage using the non-equilibrium Green function and the density functional theory, along its localized pseudo atomic orbitals. Our aim is to peruse the various nanometer-scale transport properties and eventually predict the overall quantum transport behavior of this organic mesoscopic system. We investigate the density of states, transmission spectrum, molecular orbitals, current–voltage characteristics, rectification ratio, and differential conductance characteristics at discrete bias voltages to get the insight about various transport phenomena. The observed results elucidate that the quantum tunneling causes the electron transport in this molecular bridge and becomes prominent due to strong mechanical interactive coupling between the molecule and the electrodes having low HOMO–LUMO (highest occupied molecular orbital–lowest unoccupied molecular orbital) gap of 0.55 eV. We conclude that Au–C20–Au device exhibited metallic nature forming the current coulomb staircase with transition points at ±1 V and the quantum conductance of order 2G0 at low bias voltages.