Azobenzene derivatives, which can change their conformation between cis and trans stereoisomers upon ultraviolet or visible light irradiation, have attracted considerable attention in the designs of single-molecule functional device. The electronic transport properties of azobenzene and azonaphthalene molecular junctions are investigated by using the density functional theory and non-equilibrium Green's function method . The calculations demonstrate that the azobenzene and azonaphthalene molecular junctions with asymmetric thiol anchoring groups show excellent rectification properties. In addition, the low-bias switching ratio of the molecular junctions during the cis-trans stereoisomerization transformations is significantly enhanced. The electronic transport properties of the molecular systems are dominated by the lowest unoccupied molecular orbitals (LUMOs). In the negative bias regime, the LUMO-contributed transmission peaks move away from the Fermi level, thereby suppressing the transmission probability of the azo molecular junctions. This mechanism is responsible for the high rectification ratio of the azobenzene and azonaphthalene molecular junctions. The numerical results show that, for the molecular junctions with "off" states, the contacts between the molecules and the drain electrodes are located near the nodes of transmission eigenstates, which lead to significant destructive quantum interference effect when electrons enter the drain electrode. Therefore, controlling the quantum interference of the electron wave can effectively enhance the switching and rectification performance of the molecular junction. Side-substituent not only enhances the low-bias rectification performance of the trans- azonaphthalene molecular junctions, but also results in the reverse of stereoisomeric switch of the azonaphthalene molecular junction under positive and negative biases. This property can be used to design single-molecule logic circuits. Compared with the caluculations of the HSE06 hybrid functional, the HOMO-LUMO energy gaps caluculated with the PBE functional are relatively smaller, which results in higher current values. Consequently, the rectification characteristics obtained using the HSE06 hybrid functional shift towards the higher bias region compared to those obtained using the PBE functional.