Both the randomness of the seismic motion and the dam structural parameters have an important impact on the stability and reliability of gravity dams. In this paper, the anti-sliding stability limit state equation of the construction foundation surface of gravity dam was established, with the maximum values of the horizontal and vertical inertial force of the dam body in the stochastic process as the random variables. By the determination of the mean and variance of the random variables according to the parameters of the stochastic process, the dual randomness problems of seismic load and structural parameters were merged into one random variable mode. Then, the JC method was used to analyze the reliability of the anti-sliding stability of the foundation surface of a gravity dam in an actual project, and the failure probability of the anti-sliding stability of the gravity dam was analyzed based on the probability of earthquake occurrence. Finally, the sensitivity of random parameters of each structure to reliability and failure probability was analyzed by orthogonal test method. The results show that the proposed method with the maximum value of the stochastic process as the random variable can be used for the analysis of the reliability of the anti-sliding stability of gravity dams under the double random situation of seismic motion and structural parameters. The reliable index of anti-sliding stability along the foundation surface of this concrete gravity dam was 4.23, the failure probability was 0.001 17%. The friction coefficient of the foundation surface, the coefficient of cohesion and the density of the dam material had a significant impact on the reliability calculation results.