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A new mixed Poisson model is proposed as a better alternative for modelling count data in the presence of overdispersion and/or heavy-tail. The mathematical properties of the model were derived. The maximum likelihood estimation method is employed to estimate the model’s parameters and its applications to the three real data sets discussed. The model is used to model sets of frequencies that have been used in different literature on the subject. The results of the new model were compared with Poisson, Negative Binomial and Generalized Poisson-Sujatha distributions (POD, NBD and GPSD, respectively). The parameter estimates expected frequencies and the goodness-of-fit statistics under each model are computed using R software. The results show that the proposed PSD fits better than POD, NBD and GPSD for all the data sets considered. Hence, PSD is a better alternative provided to model count data exhibiting overdispersion property.