In this paper, a new distribution is introduced based on a continuous Weibull-Rayleigh distribution, that is a new three-parameter lifetime model called as the discrete Weibull-Rayleigh distribution. It is a distribution allowing for a bathtub-shaped hazard rate function. Its mathematical properties are discussed, and the estimation of model parameters is compared by the maximum likelihood and the least square methods. An actual data set of thermal aging is fitted to the new model, which shows the superiority of the proposed distribution.