Summary: To aim at the deficiencies of traditional numerical methods, a Weibull model widely adopted in the family of Bayesian accelerated failure-time models is discussed. The Markov chain Monte Carlo method based on Gibbs sampling is introduced, which is used to simulate dynamically the Markov chain of the posterior distributions of the related parameters for randomly truncated constant-stress accelerated life testing. Also, the Bayesian estimators of the applied parameters are given. The results of data simulations are utilized to show the process of setting the model by using the BUGS package. This proves the validity of the proposed model.