A four level ladder scheme is employed for the realization of slow light large Kerr nonlinear indices in an asymmetric semiconductor three-coupled-quantum-well (TCQW) structure based on intersubband transitions. It is shown that a giant Kerr nonlinearity accompanied with negligible loss can be achieved by properly tuning the intensity of the control fields. A dressed state analysis is given to explain the origin of such a transparency based on slow light enhanced Kerr nonlinearity in this solid medium. In addition, we show that the three-photon detuning plays the important role in enhancing the third-order nonlinearity of the TCQW medium, and may provide new possibilities for technological applications in nonlinear optics and optical switching.