Based on the generalized rheological model of viscoelastic materials, a generalized damping model and the dynamic equilibrium equation of structure are derived. The exponential function and Gaussian function are selected as the convolutional kernel functions of the generalized damping model. The seismic response of the Koyna Dam is calculated by the Newmark direct integration method, and the effects of relaxation parameter and time integration step on the seismic response of the dam are also analyzed. Seismic responses of the dam with the generalized damping model and the viscous damping model are compared at last. The results show that the seismic peak response with the generalized damping model is greater than that with the viscous damping model, and the larger the relaxation parameters, the closer the peak response with the generalized damping is to that with the viscous damping. Meanwhile, the exponential model has higher requirements for the time step of numerical integration than the Gaussian model.