This study aims to propose a seismic performance analysis framework based on the oblique incidence theory, estimate a normalized damage response (RDVR) through seismic parameters and incident angles, and explore the variation in dynamic responses of concrete dams with arbitrary incident angles under near-fault vertically polarized shear (SV) waves. Several near-fault pulse-like records were selected, and their decomposed nonpulse (residual) components were used to guarantee the similarity of the response spectra. Furthermore, a seismic input model of the SV wave oblique incidence was developed based on the viscous-spring artificial boundary method, and its accuracy was verified using a numerical application. The effects of the incident angles of SV waves (-30 degrees to 30 degrees at 5 degrees intervals), seismic intensity, and polarity on the damage and displacement responses of a gravity dam-reservoir-foundation system under pulse-like and nonpulse motions were studied. Additionally, the relationships between the incident angle, seismic characteristics [including the peak ground velocity to peak ground acceleration (PGV/PGA) ratio and spectral acceleration S-a(T-1)], and the proposed RDVR were established. The most unfavorable incidence angles for different cases were derived. The numerical results showed that the negative direction (from downstream to upstream) has a significant effect on the nonlinear responses of a dam. The seismic features of PGV/PGA exhibited a better correlation with RDVR than S-a(T-1). Subsequently, the damage to the gravity dam was estimated using the multivariate fitted method according to the proposed prediction model. The results showed that the proposed prediction model with arbitrary incident angles provides a good estimation of the real results. Thus, it is important to consider the coupled effect of incident angles and seismological characteristics in the seismic assessment of concrete dams located in near-fault regions.