Abstract: To analyze the time-history reliability of aseismatic structures, an algorithmbased on the genetic simulated annealing and time-history methods was proposed on the basis of the characteristic of structural performance functions for the time-history reliability of aseismatic structures,i. e.they are implicit functionswith strong non-linearity. This algorithm can reflect the randomness of structural parameters and earthquake motions and the effects of an earthquake action and static loads. Furthermore, time-history reliability index of aseismatic structures at any time in the process of an earthquake can be got by using the algorithm. As an example, the time-history reliability of story-drift capacity for a three-story reinforced concrete (RC) frame respectively under frequent and strong earthquakes was analyzed using the algorithm and the Monte Carlo method, and the result shows the effectiveness of the algorithm.