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The Kumaraswamy InverseWeibull distribution has the ability to model failure rates that have unimodal shapes and are quite common in reliability and biological studies. The three-parameter Kumaraswamy InverseWeibull distribution with decreasing and unimodal failure rate is introduced. We provide a comprehensive treatment of the mathematical properties of the Kumaraswany Inverse Weibull distribution and derive expressions for its moment generating function and the <i>r</i>-th generalized moment. Some properties of the model with some graphs of density and hazard function are discussed. We also discuss a Bayesian approach for this distribution and an application was made for a real data set.