Statisticians have developed and proposed new families of distributions by extending or generalizing the existing ones. These families of distributions are extended by adding one or more parameters to the baseline distributions to make it more flexible in fitting different kinds of data. In this study, a new four-parameter lifetime family of distributions called the Extended Topp Leone Generalized Exponentiated-G family of distributions was introduced by using the T-X methodology which has been proposed in the literature. Some mathematical properties of the class of distributions such as the moments, moment generating function, quantile function, survival, hazard, reversed hazard and odds functions and Renyi entropy were presented. The estimation of the parameters by maximum likelihood method was discussed. Two sub-models such as extended Topp Leone generalized exponentiated exponential and extended Topp Leone generalized exponentiated Weibull distributions were discussed. An application of extended Topp Leone generalized exponentiated exponential distribution to a real life data set representing the relief times (in minutes) of patients receiving an analgesic was used to show the fit and flexibility of the new distribution over some lifetime distributions in literature. The results showed that the new distribution fits better in this data than the competing models considered.