Electric-field-induced birefringence of a polymer-stabilized blue-phase liquid crystal (BPLC) is investigated. In the low field region, conventional Kerr effect holds. As the electric field increases, the induced birefringence gradually saturates and deviates from Kerr effect. An exponential convergence model, called extended Kerr effect, is proposed to fit the experimental data. Good agreement between experiment and model is obtained. This extended Kerr effect will make a significant impact to the optimization of emerging BPLC display devices