In this study, a new family of distributions called the type II Topp-Leone is introduced and three new special models are presented. Some mathematical properties of the type II Topp-Leone family are studied. Explicit expressions for the moments, probability weighted, quantile function, mean deviation, order statistics, Renyi and Shannon entropies are investigated. Parameter estimates of the family are obtained based on the maximum likelihood procedure for both uncensored and censored data. A simulation study is conducted to show the performance of the new family. Then, two real data sets based on censored and uncensored data sets are employed to show the usefulness of the new family.