A new four-parameter lifetime model called the Weibull Fréchet distribution is defined and studied. Various of its structural properties including ordinary and incomplete moments, quantile and generating functions, probability weighted moments, Rényi and δ-entropies and order statistics are investigated. The new density function can be expressed as a linear mixture of Fréchet densities. The maximum likelihood method is used to estimate the model parameters. The new distribution is applied to two real data sets to prove empirically its flexibility. It can serve as an alternative model to other lifetime distributions in the existing literature for modeling positive real data in many areas.