In this study, a new four-parameter lifetime distribution called the Topp Leone KumaraswamyWeibull distribution was derived using the Topp-Leone Kumaraswamy-G family of distributions.  The model includes several important sub-models as special cases such as Topp-Leone exponentiatedWeibull,Topp Leone Weibull, exponentiatedWeibull and Weibull distributions. An expansion for the probability distribution function was carried out which was used to derive some of the mathematical properties. Some mathematical properties of the distribution were presented such as moments, moment generating function, quantile function, survival function, hazard function as well as mean, 1st quartile, median and 3rd quartile. The probability distribution function of order statistics of the Topp-Leone KumaraswamyWeibull distribution was obtained. Estimation of the parameters by maximum likelihood estimation method was discussed.  Two real-life application of the distribution was presented and the analysis showed the fit and flexibility of the new distribution over some lifetime models considered. The analysis showed that the model is effective in fitting biomedical data.