We propose a new class of continuous distributions called the generalized Kumaraswamy-G family which extends the Kumaraswamy-G family defined by Cordeiro and de Castro (2011). Some special models of the new family are provided. Some of its mathematical properties including explicit expressions for the ordinary and incomplete moments, generating function, Renyi entropy, order statistics and characterizations are derived. The new location-scale regression model is introduced based on the new generated distribution. The maximum likelihood is used for estimating the model parameters. The flexibility of the generated family is illustrated by means of two applications to real data sets.