In this study, we propose a new three-parameter lifetime model based on the type-I half-logistic G family and the unit-Gompertz model, which we named the half-logistic unit Gompertz type-I distribution. The key feature of such a novel model is that it adds a new tuning parameter to the unit-Gompertz model using the type-I half-logistic family in order to make the unit-Gompertz model more flexible. Diagrams and numerical results are used to look at the new model’s mathematical and statistical aspects. The efficiency of estimating the distribution parameters is measured using a variety of well-known classical methodologies, including Anderson–Darling, maximum likelihood, least squares, weighted least squares, right tail Anderson–Darling, and Cramer–von Mises estimation. Finally, using the maximum likelihood estimation method, the flexibility and ability of the proposed model are illustrated by means of re-analyzing two real datasets, and comparisons are provided with the fit accomplished by the unit-Gompertz, Kumaraswamy, unit-Weibull, and Kumaraswamy beta distributions for illustrative purposes.