In this paper, the convolution type nonviscous damping model with exponential kernel function is used to establish the vibration equation of nonviscous damping structures under the seismic excitation. By introducing the state variables, the statespace expression of the vibration equation of nonviscous damping structure is derived. Taking a gravity dam as an example, the seismic response of the nonviscous damped dam is solved by the refined timedomain integration method under the Koyna seismic excitation, and the response time history of the dam is given for different values of the relaxation parameter μ. The results show that the peak response of the nonviscous damping model is larger than that of the viscous damping model whether it is empty or full, and the peak response of the nonviscous damping model is increased with the decrease of μ, which indicates that the damping effect of the viscous damping model is larger than that of the nonviscosity damping model. Therefore, the peak response of concrete gravity dam may be underestimated by using the viscous damping model in the seismic response analysis, thereby affecting the safety and rationality of the structural design scheme.