This paper proposed a truncated family of probability distributions named the doubly truncated Zubair-generalized family of truncated distributions. Certain properties of doubly truncated Zubair-Generalized family of truncated distributions are worked on. These properties are the quantile, median, the non-central moments, central moments, order statistics, entropy measures such as R$\acute{e}$nyi, Shannon, Tsallis entropies, also the mean residual life, mean past lifetime and mean time to failure. The doubly truncated Zubair-Weibull distribution is a special sub-model of the doubly truncated Zubair-generalized family. Some important statistical properties of the doubly truncated Zubair-Weibull distribution are studied, such as the reliability, hazard, reversed hazard and cumulative hazard rate functions. In addition, the moments, quantile, order statistics, entropies and some important special sub-models of the doubly truncated Zubair-Weibull distribution are given. The maximum likelihood estimation approach is applied to estimate the unknown parameters, reliability and hazard rate functions. A simulation study is conducted to evaluate the performance of the maximum likelihood estimates. Two life-time real data sets are applied to show the flexibility and applicability of the proposed model.