Statistical distributions are important in modeling the real life of an item and therefore proper distributions that provide useful information for sound conclusions and decisions are needed. For that reason, the demand for developing new generalized distributions have become appropriate for data that have both monotonic and non-monotonic hazard rate functions. In this paper, we develop a new distribution called the Type IITopp-Leone-G Power Series (TIITLGPS) distribution by compounding the Type II Topp-Leone-G (TIITLG) distribution with the power seriesdistribution. Statistical properties of the TIITLGPS distribution are obtained. A variety of shapes for the densities and hazard rate are presented of the considered special case. A simulation study to examine the efficiency of the maximum likelihood estimates is also conducted. Finally, the bladder cancer data example is analyzed for illustrative purposes, it is displayed that the introduced distribution provides better fit when compared to other non-nested distributions considered in this work.