The second harmonic suceptibility due to the intersubband transitions in the three-level GaAs/AlxGa1-xAs/AlyGa1-yAs compositionally asymmetric coupled quantum well (CACQW) under the influence of the applied electric field is investigated theoretically. The subband eigenenergy E(n) of the CACQOW structure could he designed to form an equally spaced energy-level ladder. Since the eigenenergy spacing could be designed to resonate with the pumping source, the second harmonic susceptibility could be greatly enhanced through the double resonance. Based on the theoretical calculations, the second harmonic susceptibility as high as 220 nm/V can be achieved for the CACQW. This is a more than three orders of magnitude enhancement as compared to that of the bulk GaAs. In addition to the design of CACQW structure, the double resonance can also be achieved by biasing the CACQW under a proper electric field. The extinguishment of the second order nonlinear optical effect by the applied electric field has also been studied. This phenomenon is attributed to the symmetry restoration of envelope wave functions of the CACQW structures under the quenching electric field C(off). A simple physical model to estimate the C(off) has also been developed.