A detailed investigation of the second harmonic generation in symmetrical and asymmetrical Gaussian potential quantum wells under the influence of applied electric field by using the compact-density-matrix approach and the finite difference method.The results show that the second-harmonic gener-ation susceptibility obtained in two cases can reach the magnitude of 10-4m/V,which depend dramatically on the applied electric field and the struc-tural parameters.Finally,the resonant peak and its corresponding to theresonant energy are also taken into account.