This paper presents a comprehensive investigation on Kerr nonlinearity in a three-level semiconductor quantum well (SQW) superlattice and validates the existence of large Kerr nonlinearity of the order of [Formula: see text] in the vicinity of an electromagnetically induced transparency (EIT) window. The Kerr nonlinearity is found to vary with the relative phase of the applied optical fields, and by selecting suitable relative phases, an enhanced Kerr nonlinearity can be obtained. The results may find significant applications in optoelectronic and photonic devices.