A new class of continuous distributions called theexponentiated Weibull-H family is proposed and studied. The proposed class extends the Weibull-H family of probability distributions introduced by Bourguignon et al. (J Data Sci 12:53–68,2014). Some special models of the new family are presented. Its basic mathematical properties including explicit expressions for the ordinary and incomplete moments, quantile and generating function, Renyi and Shannon entropies, order statistics, and probability weighted moments are derived. The maximum likelihood method is adopted to estimate the model parameters and a simulation study is performed. The flexibility of the generated family is proved empirically by means of two applications to real data sets.