In this paper, we discuss different predictors of times to failure of units censored in a hybrid censored sample from exponential distribution. Bayesian and non-Bayesian point predictors for the times to failure of units are obtained. Non-Bayesian prediction Intervals are obtained based on pivotal and highest conditional density methods. Bayesian prediction intervals are also proposed. One real data set has been analyzed to illustrate all the prediction methods. Finally, different prediction methods have been compared using Monte Carlo simulations.