A modified Hertz model with nonlinear damping (Hertz damp model) is proposed for capturing the seismic pounding response of adjacent structures. Relevant parameters in the model are theoretically derived and numerically verified. Then, this model is used to simulate pounding response of a base-isolated highway bridge subjected to near fault ground motions. At the same time, nonlinear viscous dampers are installed between bridge decks for pounding prevention. The appropriate damping coefficient of the dampers can be found by parametric studies. It is shown that nonlinear viscous dampers are effective in reducing the relative displacement between bridge decks. At last, the hysteresis curve, the maximal damper force and stroke are used to demonstrate the behavior of nonlinear viscous dampers. The results indicate that satisfied viscous dampers can be produced to eliminate pounding according to the current manufacturing skills.