A theoretical investigation is carried out into the impact of incoherent pumping fields and quantum interference induced by incoherent pumping fields on the Kerr nonlinearity in a three-level asymmetric semiconductor quantum well system. It is found that Kerr nonlinearity is so sensitive to the rate of incoherent pumping fields, but insensitive to the quantum interference induced by incoherent pumping fields. In addition, it is demonstrated that an enhanced Kerr nonlinearity with reduced absorption can be achieved just via the strength of Fano-type interference and without applying any coherent laser field. The obtained results are very different from the conventional schemes which coherent coupling fields are used to control the Kerr nonlinearity. This advantages make our electronic medium much more practical than its atomic counterpart due to its flexible design and the controllable interference strength.