Summary: In this paper, we introduce the exponentiated Weibull-geometric (EWG) distribution which generalizes two-parameter exponentiated Weibull (EW) distribution introduced by G. S. Mudholkar et al. [Technometrics 37, No. 4, 436–445 (1995; Zbl 0900.62531)]. This proposed distribution is obtained by compounding the exponentiated Weibull with geometric distribution. We derive its cumulative distribution function (CDF), hazard function and the density of the order statistics and calculate expressions for its moments and the moments of the order statistics. The hazard function of the EWG distribution can be decreasing, increasing or bathtub-shaped among others. Also, we give expressions for the Renyi and Shannon entropies. The maximum likelihood estimation is obtained by using EM-algorithm [A. P. Dempster et al., J. R. Stat. Soc., Ser. B 39, 1–38 (1977; Zbl 0364.62022); G.J. McLachlan and T. Krishnan, The EM algorithm and extension. New York: Wiley (1997)]. We can obtain the Bayesian estimation by using Gibbs sampler with Metropolis-Hastings algorithm. Also, we give application with real data set to show the flexibility of the EWG distribution. Finally, summary and discussion are mentioned.