In this paper, a new family of polyno-expo-trigonometric distributions is presented and investigated. A special case using the Weibull distribution, with three parameters, is considered as statistical model for lifetime data. The estimation of the parameters are performed with the maximum likelihood method. A numerical simulation study verifies that the bias and the mean squared error of the obtained maximum likelihood estimators tend to zero as the sample size is increased. Three real life data sets are then analyzed. We show that our model has a good fit in comparison to other well-known powerful models in the literature.