This paper investigates the electronic transport properties in an Aharonov-Bohm interferometer with a quantum dot coupling to left and right electrodes. By employing cluster expansions, it transforms the equations of motion of Green’s functions into the corresponding equation of motion of connected Green’s functions, which provides a natural and uniform truncation scheme. With this method under the Lacroix’s truncation approximation, it shows that the asymmetric line shape of zero bias conductance manifests itself as the Fano effect, and the Kondo effect has been observed in the narrow peak of differential conductance curve of the system. Our numerical results also show that the building of Fano state suppresses the amplitude of Kondo resonance.