In order to solve the problem of high cost of structural time-variant reliability analysis, a time-variant reliability analysis strategy based on weighted stochastic simulation was proposed. Time-variant reliability analysis needs to calculate the failure probability of structure with respect to different times, which often requires multiple reliability analyses, involving hugh calculation cost. The proposed method improves and expands the conventional stochastic simulation method which is used to analyze the static reliability problem. The weighted Monte Carlo method and weighted importance sampling method respectively are developed respectively by using the weighting strategy to efficiently analyze and calculate the time-variant reliability problem. The proposed methods require only one conventional reliability analysis simulation to obtain the estimator of time-variant failure probability function. Two examples, a tubular cantilever beam and a ten-bar truss, are used for verification. Results show that the weighted methods can greatly ease the computational burden and improve the computational efficiency while ensuring the precision.