An effective method for evaluating the damage probability of concrete gravity dams under ground motions with different intensities is fragility analysis. The fragility analysis of gravity dams generally assumes that seismic waves are vertically incident, but those in the near-fault area are obliquely incident. The oblique incidence of seismic waves has a considerable influence on the seismic response of gravity dams. Based on the database of the Pacific Earthquake Engineering Research Center, 16 ground motion records were selected, and the oblique incidence input of SV waves was realized using the viscoelastic artificial boundary and equivalent nodal load. The PGA of ground motion was modulated using the incremental dynamic analysis method. The Koyna concrete gravity dam in India was taken as the research object in this paper. The fragility curves for different earthquake damage levels of the gravity dam under the oblique incidence of SV waves were established by taking the relative displacement of the dam crest as the seismic performance index. Results show that under the same earthquake damage level and ground motion intensity, the damage probability of gravity dams under the oblique incidence of SV waves decreases compared to that under the vertical incidence. When the PGA is close to the actual earthquake intensity of gravity dams, the maximum reduction rates of failure probability are 27.3% and 68.2%, respectively, when the incident angles are 15° and 30°, compared with that under vertical incidence. Meanwhile, the maximum difference values of failure probability are 36.6% and 83.9% compared with those under vertical incidence. Therefore, the influence of the oblique incidence of seismic waves should be considered in the seismic performance analysis of concrete gravity dams. The results can also provide a reference for the safety risk assessment of concrete gravity dams in near-fault areas.