We introduce a new class of continuous distributions called the generalized transmuted-Gfamily which extends the transmuted-Gclass. We provide six special models of the new family. Some of itsmathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Rényi and Shannon entropies, order statistics and probabilityweighted moments are derived. The estimation of the model parameters is performed by maximum likelihood. The flexibility of the proposed family is illustrated by means of three applications to real data sets.