In this paper, we attempt to introduce a new lifetime model as a discrete version of the continuous exponentiated exponential distribution which is called discrete exponentiated exponential distribution (DEE). The introduced model contains geometric distribution as a special case. Some basic distributional properties, moments, reliability indices, probability function, characteristic function, and order statistics of the new model are discussed. Estimation of the parameters is illustrated using the maximum likelihood method and moment method. The model with three real data set is also examined.