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Unified hybrid censoring scheme is a mixture of generalized Type-I and Type-II hybrid censoring schemes. In this paper, we mainly consider the analysis of unified hybrid censored data when the lifetime distribution of the individual item is a two-parameter generalized exponential distribution. It is observed that the maximum likelihood estimators can not be obtained in a closed form. We obtain the maximum likelihood estimates of the parameters by using Newton-Raphson algorithm. The Fisher information matrix has been obtained and it can be used for constructing asymptotic confidence intervals. We also obtain the Bayes estimates of the unknown parameters under the assumption of independent gamma priors using the importance sampling procedure. Simulations are performed to compare the performances of the different schemes and one data set is analyzed for illustrative purposes.