This paper introduces a new discrete compound probability distribution, named the Poisson-New Quadratic-Exponential Distribution (PNLED), which is derived by mixing the Poisson distribution with the New Quadratic-Exponential distribution. The PNLED is designed to be a better alternative to the Poisson-Lindley distribution (PLD), Poisson Mishra distribution (PMD), and Poisson-Modified Mishra distribution (PMMM) for modeling over-dispersed count data. The authors derive the probability mass function (pmf), probability generating function (pgf), and moment generating function (mgf) of the PNLED. They also calculate the first four moments about the origin and the mean to analyze the distribution's shape, size, and variability. The central moments are derived to confirm that the PNLED is over-dispersed, positively skewed, and leptokurtic. The paper discusses two methods for estimating the parameter of the PNLED: the method of moments and maximum likelihood. Finally, the goodness of fit of the PNLED is tested using four examples of over-dispersed count data from various fields, and the results show that the PNLED outperforms the PLD, PMD, and PMMD in terms of fit. The authors conclude that the PNLED is a valuable tool for statistical modeling of over-dispersed count data.This paper introduces a new discrete compound probability distribution, named the Poisson-New Quadratic-Exponential Distribution (PNLED), which is derived by mixing the Poisson distribution with the New Quadratic-Exponential distribution. The PNLED is designed to be a better alternative to the Poisson-Lindley distribution (PLD), Poisson Mishra distribution (PMD), and Poisson-Modified Mishra distribution (PMMM) for modeling over-dispersed count data. The authors derive the probability mass function (pmf), probability generating function (pgf), and moment generating function (mgf) of the PNLED. They also calculate the first four moments about the origin and the mean to analyze the distribution's shape, size, and variability. The central moments are derived to confirm that the PNLED is over-dispersed, positively skewed, and leptokurtic. The paper discusses two methods for estimating the parameter of the PNLED: the method of moments and maximum likelihood. Finally, the goodness of fit of the PNLED is tested using four examples of over-dispersed count data from various fields, and the results show that the PNLED outperforms the PLD, PMD, and PMMD in terms of fit. The authors conclude that the PNLED is a valuable tool for statistical modeling of over-dispersed count data.