This paper introduces a new generalization of the transmuted additive Weibull distribution by Elbatal and Aryal [10], based on a new family of lifetime distribution. We refer to the new distribution as a new transmuted additive Weibull (NTAW) distribution. The new model contains some of lifetime distributions as special cases such as the transmuted additive Weibull, exponentiated modified Weibull, exponentiated Weibull, exponentiated exponential, transmuted Weibull, Rayleigh, linear failure rate and exponential distributions, among others. The properties of the new model are discussed and the maximum likelihood estimation is used to evaluate the parameters. Explicit expressions are derived for the moments and examine the order statistics. An application to real data set is finally presented for illustration.