We introduce a new family of continuous distributions called the Poisson-exponential-G family based on the Poisson-exponential distribution of Cancho et al. (2011). The shapes of the density and hazard functions corresponding to new family are studied. Two sub-models are also discussed. We study some properties of the proposed family such as moments, generating functions, entropy measures, stress-strength model and order statistics. The model parameters are estimated via maximum likelihood approach. A Monte-Carlo simulation study is designed and used to show the performances of obtained estimators of parameters. Two real applications are introduced to show the importance of the new family.