In order to reasonably consider the effects of soil parameters variability on the probability of seepage failure for embankment dams，this paper compiles the interface implementation procedure between the seepage finite element analysis and reliability analysis of embankment dams based on GEOSTUDIO and MATLAB. A real embankment dam is investigated as an example to validate the effectiveness of the proposed approach. The influence of the variability of the hydraulic conductivity of dam materials and the fitting parameters of soil water characteristic curves on the probability of seepage failure under the rapid drawdown of reservoir water level is discussed. The results indicate that the rise of reservoir water level adversely affects the slope stability of embankment dam. The probability of seepage failure increases by nearly twice when the water level rises from the normal storage level to the spillway design flood level. The backward seepage in the dam body occurs with the rapid drawdown of reservoir water level，influenced by the matrix suction of dam material. The probability of seepage failure for the embankment dam increases sharply once it reaches a certain moment，and then it falls to a stable value until the pore water pressure is fully dissipated.