The third-order nonlinear susceptibility χ(3) of asymmetrically coupled quantum well (ACQW) structure is calculated by employing a V-type three-level model. The efficiency of absorptive optical nonlinearity, which we define as the ratio of the third-order nonlinear susceptibility χ(3) to the linear absorptive coefficient α0, is analysed for different electronic coherence oscillation frequencies. We show that the efficiency is enhanced with the increase of the electroniccoherence oscillation frequency between the two wells but is degenerated as that of a single quantum well when the electronic coherence oscillation frequency is zero. Compared with single quantum well, the ACQW designed has the property of nonlinear absorption and dispersion depending strongly on the exteal electric field along the growth direction. We predict that ACQW structures can provide both high efficiency limiters and controllable optical Kerr switch in future communication systems.