Structure reliability calculation problem which contains relevant random variables can be solved conveniently by establishing iterative formula of check point in generalized random space directly. A kind of iterative formula of check point with better convergence is derived in generalized random space; and it is applied to reliability analysis of slope stability. According to the reliability analysis of Kajiwa concrete face rockfill dam slope stability under seismic conditions

it shows that: (1) The input parameters used in safety coefficient method are determined values

so that the random fluctuation influence of parameters can not be considered in calculation. Reliability analysis can reflect the influence of randomness of parameters; it is beneficial to evaluating engineering safety and risk resistance capacity. (2)The reliability index of structure will increase by considering the earthquake and the dam slope instability probability occurring simultaneously

and the increased range is related to the probability of earthquake. (3)Nonlinear strength index of rockfill has positive correlation; the reliability of slope stability will increase when the correlation of strength index is considered.