In this paper, we provide a method for constructing an exact confidence interval and an exact joint confidence region for the parameters of the Gompertz distribution under the first failure-censored sampling plan [1]. Moreover, when compared to ordinary sampling plans, the sampling plan of Balasooriya [1] has an advantage in terms of shorten test-time and a saving of resources. Finally, we give an example to illustrate our proposed method. Results from simulation studies assessing the performance of our proposed method are included.