<p>This article presents the Bayesian approach for estimating the parameters of the Burr Type-XII distribution and the acceleration factor under a step-stress partially accelerated life test using time-censored data. The posterior means and posterior variances are obtained assuming the squared-error loss function. The Bayes estimates can not be obtained in explicit forms. Accordingly, approximate Bayes estimates are computed using Lindley’s method. The advantage of this method is presented. The approximate Bayes estimates are obtained under the assumption of non-informative priors and compared with their maximum likelihood counterparts using a Monte Carlo simulation.</p>