A new lifetime model, which extends the Weibull distribution using the generalized transmuted-G family proposed by Nofal et al. (2017), called the generalized transmuted Weibull distribution is proposed and studied. Various of its structural properties are derived. The maximum likelihood method is used to estimate the model parameters. A small simulation study is conducted. The new distribution is applied to a real data set to illustrate its flexibility. It can serve as an alternative model to other lifetime models available in the literature for modeling positive real data in many areas.