On the basis of the half‐Cauchy distribution, we propose the called beta‐half‐Cauchy distribution for modeling lifetime data. Various explicit expressions for its moments, generating and quantile functions, mean deviations, and density function of the order statistics and their moments are provided. The parameters of the new model are estimated by maximum likelihood, and the observed information matrix is derived. An application to lifetime real data shows that it can yield a better fit than three‐ and two‐parameter Birnbaum‐Saunders, gamma, and Weibull models.