We introduce a new generalization of Weibull distribution by making use of a transformation of the standard two-sided power distributed random variable. Weibull and the exponentiated Weibull distributions are sub-models of this new distribution. We show that this newly defined distribution is in fact a mixture of the truncated forms of Weibull and the exponentiated Weibull distributions. The new distribution has two shape parameters that make it more flexible for modeling data than Weibull and exponentiated Weibull distributions. We study its properties, consider the maximum likelihood estimation procedure and apply it on some real data sets from reliability.