Bayesian updating of the reliability of deteriorating engineering structures based on inspection data has been attracting a lot of attention recently because it can provide more accurate estimates of the structural reliability with the number of inspection data increases. Based on Bayesian theory, the prior distributions of uncertain parameters associated with the random variable of interest can be updated by combining with the inspection data which is related to the likelihood function. Then, the posterior distribution of the random variable of interest can be obtained using the total probability theorem. Typically, the posterior distribution of the random variable of interest is difficult to obtain due to the multi-dimensional parameter space and complex integration function of the Bayesian updating model. This paper presents a new effective method for obtaining the posterior distribution of the random variable of interest and its time-variant reliability evaluation. According to the proposed method, the Smolyak-type quadrature formula is applied first to obtain the first three moments (i.e., mean, standard deviation, and skewness) of the updated uncertain parameters. Then, the posterior probability distributions of the uncertain parameters are approximated using the three-parameter lognormal distribution. Finally, the posterior probability distribution of the random variable is constructed from the first three posterior moments of the random variable, which are calculated by utilizing the Smolyak-type algorithm twice consecutively. Numerical example demonstrates that the results of the proposed methodology are almost the same as those of the Markov chain Monte Carlo simulation, whereas the structural reliability could be misestimated without considering Bayesian updating.