A pseudo analytical method for time-dependent system reliability analysis of nonlinear stochastic structural dynamics is investigated. This method is a class of linearization approaches that linearize approximately a nonlinear state vector equation to a discrete Gaussian and Markovian state vector equation, and the optimal state vector and covariances at times k and k+1 are estimated by the Kalman Filter algorithm with a set of numerically obtained response data. In this way, the probability of performance may be evaluated. Finally, a numerical example of a nonlinear structural system is demonstrated in order to examine the efficiency of the method.