In this paper, the researchers attempt to introduce a new generalization of the exponential distribution. This new model is obtained by compounding the exponential distribution and discrete generalized exponential distribution of a second type, which is a generalization of the geometric distribution. The new introduced model contains the exponential-geometric distribution as a special case. Some basic distributional properties, moments and order statistics of the new model are discussed. Estimation of the parameters is illustrated, using the maximum likelihood method, and the model with a real data set is also examined.