The nonlinear time-history analysis is the most suitable method to depict the seismic response of a concrete gravity dam. Also, ground motion selection is an important aspect of seismic analysis. This study focuses on the seismic response analysis of Koyna Dam–foundation system. The material nonlinearity is specified to the dam and foundation using the concrete damaged plasticity model and Mohr–Coulomb failure model, respectively. The 2D finite element model of the dam–foundation system is analyzed using ABAQUS. The infinite elements are used for the finite element analysis of the unbounded domain of foundation. The seismic analysis is conducted for ten ground motions that are selected using the conditional mean spectrum approach. Additionally, the ten ground motions are modified using the spectrum compatible method, and the effect of the horizontal component of earthquake ground motion is considered for the dynamic analysis. The damage indices are evaluated based on damage dissipation energy and crack length. Meanwhile, the damage index value shows the global damage states of the gravity dam, and it can be considered as a damage measure parameter for the seismic analysis. The importance of the conditional mean spectrum approach over the spectrum compatible method is also discussed. It is concluded that the earthquake frequency content significantly influences the seismic response of the gravity dam.