We consider estimation of unknownparameters of a Burr XII distribution based on progressively Type I hybrid censored data. Themaximum likelihood estimates are obtained using an expectationmaximization algorithm. Asymptotic interval estimates are constructed from the Fisher information matrix. We obtain Bayes estimates under the squared error loss function using the Lindley method and Metropolis–Hastings algorithm. The predictive estimates of censored observations are obtained and the corresponding prediction intervals are also constructed. We compare the performance of the different methods using simulations. Two real datasets have been analyzed for illustrative purposes.