In this paper, a discrete analog of the beta-Weibull distribution is studied. This new distribution contains several discrete distributions as special sub-models. Some distributional and moment properties of the discrete beta-Weibull distribution as well as its order statistics are discussed. We will show that the hazard rate function of the new model can be increasing, decreasing, bathtub-shaped and upside-down bathtub. Estimation of the parameters is illustrated and the model with a real data set is also examined.