Our purpose in this study includes introducing a new family of distributions as an alternative to beta-G (B-G) distribution with flexible hazard rate and greater reliability which we call Truncated Weibull-G (TW-G) distribution. We shall discuss several submodels of the family in detail. Then, its mathematical properties such as expansions, probability density function and cumulative distribution function, moments, moment generating function, order statistics, entropies, unimodality, stochastic comparison with the B-G distribution and stress-strength reliability function are studied. Moreover, we study shape of the density and hazard rate functions, and based on the maximum likelihood method, estimate parameters of the model. Finally, we apply the model to a real data set and compare B-G distribution with our proposed model.