The second-harmonic susceptibilities of asymmetric coupled quantum wells (ACQW) and compositionally asymmetric coupled quantum wells (CACQW) under the influence of the applied electric field are investigated theoretically. Analytic forms of the second-harmonic susceptibility are derived by using the density matrix formalism. Coupled one-dimensional Schrodinger equation and Poisson's equation ae solved self-consistently to find the subband eigenenergies and the envelope wavefunctions for the ACQW and CACQW structures. Dipole moment matrix elements for the ACQW and CACQW are evaluated from the resulting envelope wavefunctions and large nonlinear optical effects are predicted for these two structures. Based on the theoretical calculations, the second-harmonic susceptibilities of 50 nm/V and 35 nm/V can be achieved for the ACQW and the CACQW, respectively. This is more than two orders of magnitude enhancement as compared to that of the bulk GaAs. By a suitable choice of the composition of CACQW, a novel structure which the second-order nonlinear optical effect can be turned on or off by the applied electric field is proposed based on the results of the theoretical calculation. This phenomenon is attributed to the symmetry restoration of envelope wavefunctions of the CACQW under the quenching electric field F-off. A simple physical model to estimate the F-off has also been developed successfully.