A theoretical investigation is carried out into the Kerr nonlinear effect of an asymmetric double quantum dots system. Using voltage tunneling, electromagnetically induced transparency can appear synchronously at two different frequency windows. By tuning tunneling voltage and control field suitably, the absorption property is significantly modified and therefore the enhanced Kerr nonlinearity without liner and nonlinear absorption occurs at one of the transparent windows. Analysis shows that voltage controlling between two quantum dots is key factor of the enhancement of Kerr nonlinearity.