Abstract: We propose a two-parameter generalized exponential distribution with closed-form expression based on the maximum Rényi entropy principle under the normalization and mean constraints, which is referred as the q-exponential distribution. The statistical properties of this distribution are investigated. The maximum likelihood method and information likelihood method are used to estimate the parameters of the proposed distribution, respectively. Two well-known data sets are employed to evaluate the q-exponential distribution, and the experimental results demonstrate that the proposed distribution can fit the data sets better than other well-known distributions, such as Weibull distribution and linear failure rate distribution. Additionally, the experiment results of life estimation of the Li-ion batteries prove that compared with the exponential distribution, the proposed distribution can give more accurate prediction. In the last experiment, the estimation accuracy is improved by at least 17.857%.