Dynamic modeling and cushioning performance analysis are the basis for damper design. The present aims to provide a dynamic model and optimization method for viscoelastic damper. For this purpose, a new double-rod viscoelastic damper for high-speed impact is taken as an example to demonstrate the design process. Firstly, the structure of double-rod viscoelastic damper is described to reveal its working principle. According to the properties of mastic material, a Kelvin model with variable stiffness is established by Simulink. Secondly, the influence of key component parameters on cushioning performance was analyzed for further optimization. Thirdly, based on Simulated Annealing algorithm, the viscoelastic damper system’s left piston rod diameter, piston thickness and inner cylinder diameter are chosen as the optimization variables. The optimized viscoelastic damper’s peak cushioning force is 31% lower and its cushioning effectiveness is 28% higher. The numerical results provide theoretical recommendations for the double-rod viscoelastic damper design.