Some traditional life tests result in very few failures by the end of the test. So that to reach failure quickly test units are run at higher than usual stress conditions. This study is devoted to the estimating failure time data under step-stress partially accelerated life tests based on type I censoring. The lifetime distribution of the test items is assumed to follow Burr type distribution. The Bayesianestimates of the acceleration factor and the parameters of the lifetime distribution are obtained when the shape parameters and the acceleration factor are unknown. Numerical examples are given to study the posterior variances of the parameters and their mean square errors using Mathcad (2001). For illustrating the precision and variations of   Bayesian estimates simulation results are included for different sample sizes.