In this paper, a new four parameter lifetime distribution called the Topp Leone Weibull-Lomax distribution is introduced. Some mathematical properties of the new distribution are studied including the quantile function, ordinary and incomplete moments, probability weighted moment, conditional moments, order statistics, stocastic ordering and stress strength reliability parameter. The regression model and the residual analysis for the new model are also investigated. The model parameters are estimated by using the maximum likelihood criterion and the behavior of these estimates are examined by conducting a simulation study. We prove empirically the importance and flexibility of the new distribution in modeling four data sets.