The purpose of this paper is to introduce and study a new generated family of distributions based on the type II transformation which is called the type II exponentiated half-logistic-Gompertz-Topp-Leone-G (TIIEHL-Gom-TL-G) family of distributions. We investigate its general mathematical properties, including, hazard rate function, quantile function, moments, moment generating function, Rényi entropy and order statistics. Parameter estimates of the new family of distributions are obtained based on the maximum likelihood estimation method and their performance is evaluated via a simulation study. For illustration of the applicability of the new family of distributions, four real data sets are analyzed.