In this paper, we introduce a new lifetime distribution as an alternative to generalized Gompertz, Gompertz distribution and its modified ones. This new distribution is a special case of the family of distributions introduced by Granzotto et al. [D.C.T. Granzotto, F. Louzada and N. Balakrishnan, Cubic rank transmuted distributions: inferential issues and applications., J. Stat. Comput. Simul. 87 (2017), pp. 2760–2778]. We obtain some characteristic properties of suggested distribution such as hazard function, ordinary moments, coefficient of skewness, coefficient of kurtosis, moment generating function, quantile function and median. We discuss three different methods of estimation to estimate the parameters of proposed distribution. A comprehensive Monte Carlo simulation study is performed in order to compare the performances of estimators according to mean square errors and biases. Finally, three real data applications are performed to illustrate usefulness of suggested distribution.