In this paper we introduce a new distribution called exponentiated (Lehmann type-II) Nadarajah-Haghighi (ENH-II). This version is considered a generalization of the original distribution and is more flexible than it. The statistical distributional properties of the new model are explored, including the reliability function, hazard function, a reverse hazard function, quantile function, and moment generating function. Additionally, the paper derives the moments, incomplete moments, mean deviations, Bonferroni and Lorenz curves, and some of order statistics densities functions. The study employs the maximum likelihood estimation method to estimate the model parameters. Finally, the applicability of the proposed distribution has been demonstrated by application to real data. The application showed the flexibility of the proposed distribution and its superiority over similar distributions,