In this paper, the concept of unit generalized Gompertz (UGG) distribution will be introduced as a new transformed model of the unit Gompertz distribution, which contains the unit Gompertz distribution as a special case. We calculate explicit expressions for the moments, moment generating, quantile, and hazard functions, and Tsallis and R'{e}nyi entropy. Some different methods for estimation and inference about model parameters are presented too. To estimate the unknown parameters of the model, the maximum likelihood, maximum product spacings, and bootstrap sampling have been discussed, and also approximate confidence interval is presented. Finally, a simulation study and an application to a real data set are given.