A three-parameter generalization of the Gumbel distribution, which we call Gumbel-geometric distribution, is defined and investigated. The shape of the density and hazard function is examined and discussed. Explicit expressions for the moment generating function, the characteristics function and the rth order statistic are obtained. Other properties of the distribution are also discussed. The method of maximum likelihood is proposed for the estimation of the parameter of the model and discussed. A simulation experiment is carried out to examine the asymptotic properties of the distribution. The result shows that the MSE decreases to zero as while the bias either increases or decreases (depending on the sign) for each of the parameters. The new distribution is applied to two datasets and compared to some existing generalization to illustrate its flexibility.