A Poisson regression model is commonly used to model count data. The Poisson model assumes equidispersion, that is, the mean is equal to the variance. This assumption is often violated. In count data, overdispersion (the variance is larger than the mean) occurs frequently due to excessive zeroes in the response variable. Zero-inflated Poisson (ZIP) and Hurdle models are commonly used to fit data with excessive zeros. Although some studies have compared the ZIP and Hurdle models, the results are inconsistent. This paper aims to evaluate the performance of ZIP and Hurdle Poisson models for overdispersion data through both simulation study and real data. Data were simulated with three different sample sizes, six different means, and three different probabilities of zero with 500 replications. Model goodness-of-fit measures were compared by using Akaike Information Criteria (AIC). Overall, the ZIP model performed relatively the same or better than the Hurdle Poisson model under different scenarios, but both ZIP and Hurdle models are better than the standard Poisson model for overdispersion in count data.