This is a compound probability distribution based on a single parameter and it has been obtained by compounding Poisson distribution with Modified Mishra distribution of Sah (2022). The proposed distribution is named as Poisson-Modified Mishra Distribution (PMMD). The essential characteristics of the proposed distribution have been obtained. The method of moments and the method of maximum likelihood have been discussed to obtain an estimator of the proposed distribution. Applying goodness of fit to some over-dispersed data sets for the verification of the validity of the theoretical work, we conclude that the proposed distribution would be a better alternative of Poisson-Lindley distribution (PLD) of Sankaran (1970) and Poisson-Mishra distribution (PMD) of Sah (2017).