Maximum likelihood and Bayes estimators are obtained for the three-parameter generalized Gompertz distribution, as well as the survival and hazard rate functions, using progressive first-failure censoring scheme. Two-sided approximate confidence intervals for the unknown parameters and reliability characteristics are constructed. Using gamma conjugate priors, the Bayes estimators are developed relative to both symmetric and asymmetric loss functions. However, since the Bayes estimators cannot be obtained in explicit forms, Markov chain Monte Carlo techniques are used in order to compute the Bayes estimates and associated highest posterior density credible intervals. A practical example using real-life data set is discussed for illustration purposes. Finally, to assess the performance of the proposed estimators, numerical results using Monte Carlo simulation study were reported.