We investigate the electronic transport properties of the single-impurity Anderson model. By employing the cluster expansions, the equations of motion of Green’s functions are transformed into the corresponding equation of motion of connected Green’s functions, which contains the correlation of two conduction electrons beyond the Lacroix approximation. With the method we show that the asymmetric line shape of zero bias conductance manifests itself as the Fano effect, and the Kondo effect is observed in the narrow peak of differential conductance curve of the system.The Fano and the Kondo effects can coexist in the single-impurity Anderson model when the impurity level is adjusted to an appropriate position.