In this paper, a Cubic Transmuted Kappa distribution (CTKD) to expand the work of cubic transmuted distribution families CTKD increases the ability of the transmuted distributions to be flexible and facilitate the modelling of more complex data. Some statistical properties of CTKD are discussed. To estimate the parameters for model, the maximum likelihood estimation technique in order to appear the interest of the Cubic Transmuted Kappa Distribution, two real datasets are used to examine the ability to apply it and to observe the performance of estimation techniques on CTKD, Kappa and transmuted Kappa distributions. The observed results showed that CTKD gives better fit than Kappa and transmuted Kappa distributions for the applied data sets.