According to the contact relationship between the ball and localized defect with different shapes, a contact stiffness model for the ball-defect edge contact based on Hertzian contact theory is presented, as well as the time-varying displacement model in the defect zone. A new dynamic model coupling time-varying excitations for a lubricated ball bearing with a localized defect on its races is proposed considering the lubricating film oil. This model can formulate the time-varying excitations including the time-varying displacement excitation when the ball passing over the defect zone and the time-varying contact stiffness between the ball and the defect cylindrical edges. The proposed model is applied to investigate the effect of the defect edge shape on the vibration characteristics of the ball bearing. The numerical results show that the proposed model can describe the effect of the changes in the edge shape of the defect on the vibration characteristics of the ball bearing, which cannot be formulated by the previous sharp defect edge models in the literature. It seems that the proposed method can provide some new approach for predicting accurate vibration characteristics of the ball bearing with a localized defect on its races. It also can provide some theoretical foundations for accurate ball bearing fault defection and diagnosis.