A new probability model for positively skewed datasets like economic data, medical, engineering and other sciences was developed in this paper. The new distribution is named the Topp-Leone Flexible Weibull distribution and it was generated using the Topp-Leone-G family of distributions. This new distribution has three parameters and it is very flexible in fitting several and different datasets. Its basic mathematical properties were studied and the method of maximum likelihood estimation was used for the estimation of model parameters. A real life dataset was used to illustrate the flexibility of the distribution and it was found that the new model provides a better fit to real life datasets than the Topp Leone Burr XII, Topp Leone Lomax and Exponentiated Generalized Flexible Weibull distributions.