Abstract: A negative binomial-beta exponential distribution is a new mixed negative binomial distribution obtained by mixing the negative binomial distribution with a beta exponential distribution. The generalized Waring and Waring and Yule distributions are presented as special cases of this negative binomial-beta exponential distribution. Various structural properties of the new distribution are derived, including expansions for its factorial moments, moments of the order statistics and so forth. We discuss maximum likelihood estimation method for estimating parameters of this distribution. The usefulness of the new distribution is illustrated through a real count data.