In this paper we defined a new lifetime model called the the Exponentiated additive Weibull (EAW) distribution. The proposed distribution has a number of well-known lifetime distributions as special submodels, such as the additive Weibull, exponentiated modified Weibull, exponentiated Weibull and generalized linear failure rate distributions among others. We obtain quantile, moments, moment generating functions, incomplete moment, residual life and reversed Failure Rate Functions, mean deviations, Bonferroni and Lorenz curves. The method of maximum likelihood is used for estimating the model parameters. Applications illustrate the potentiality of the proposed distribution.