A generalization of the exponentiated modified Weibull distribution so-called the transmuted exponentiated modified Weibull distribution is proposed and studied. Various structural properties including explicit expressions for the moments, quantiles, and moment generating function of the new distribution are derived. The estimation of the model parameters is performed by least square method. We hope that the new distribution proposed here will serve as an alternative model to the other models which are available in the literature for modeling positive real data in many areas.