In this article, we propose a new three-parameter Fréchet distribution named the odd Lindley Fréchet distribution. The new model can be expressed as a linear mixture of Fréchet densities. We provide some of its mathematical properties. The estimation of the model parameters is performed by the maximum likelihood method. The importance and usefulness of the proposed distribution for modeling data are illustrated using two real data sets by comparison with some other extentions of the Fréchet distribution.