In the current paper, estimation of the unknown parameters of the Gompertz distribution is considered using different methods of estimation based on simple random sampling (SRS), ranked set sampling (RSS), and folded ranked set sampling (FRSS). Methods of estimation will be considered including maximum likelihood (ML) and Bayes estimation. A comprehensive Monte Carlo simulation study is carried out to compare the resultant estimators via their biases and relative efficiencies (RE). A real data example is presented for illustration. The uniqueness of this study is that there is no parameter estimation study based on RSS and FRSS under the Gompertz distribution in the literature. The results indicate that FRSS outperforms both estimators and all sampling schemes in terms of bias. According to the relative efficiency, the ML and Bayes estimators are quite competitive.