A multilevel moving particles method is developed for the estimation of failure probabilities that are computed from numerical approximations of the performance function. The algorithm balances the statistical error of the estimate and the approximation error. This is achieved by computing a telescoping sum of estimates for the difference in the number of moves at subsequent levels of the approximation error. The sample variance of these estimates decreases with decreasing approximation error. Thus, the number of samples that has to be evaluated with high accuracy is reduced compared to a single level computation. Therefore, the proposed algorithm is very efficient for structural reliability analysis problems, in which highly accurate evaluations of the performance function are necessary and require a huge computational effort.