Journal of Mathematics (2314-4785) In this article, a new approach is used to introduce an additional parameter to a continuous class of distributions. The new class is referred to as a new extended-F family of distributions. The new extended-Weibull distribution, as special sub-model of this family, is discussed. General expressions for some mathematical properties of the proposed family are derived and maximum likelihood estimators of the model parameters are obtained. Furthermore, a simulation study is provided to evaluate the validity of the maximum likelihood estimators. Finally, the flexibility of the proposed method is illustrated via two applications to real data and the comparison is made with the Weibull and some of its well-known extensions such as Marshall-Olkin Weibull, alpha power transformed Weibull and Kumaraswamy Weibull distributions.