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This paper deals with Bayesian analysis of two-parameter generalized exponential distribution in proportional hazards model of random censorship. It is well known for two-parameter lifetime distributions that continuous conjugate priors for the parameters do not exist; we assume independent gamma priors for the scale and shape parameter. It is seen that the closed-form expressions for the Bayes estimators cannot be obtained; we suggest Tierney-Kadane’s approximation to obtain the Bayes estimates. However with this method, it is not possible to construct the HPD credible intervals, we propose Gibbs sampling procedure to approximate the Bayes estimates and also to construct the HPD credible intervals. Monte Carlo simulation is carried out to observe the behavior of the proposed methods and to compare with maximum likelihood method. One real data analysis is performed for illustration.