This paper presents a statistical model appropriate for traffic accidents, which are of count data. Since a Poisson regression model has a very strict assumption that the mean of data is equal to its variance, a negative binomial regression model (NBR) is typically preferable to use when the variance is larger than the mean. The NBR, however, is problematic to estimate when the variance is smaller than the mean. Thus, a generalized Poisson regression model (GPR) for traffic accidents is developed, which can be adoptable regardless of overdispersion or underdispersion. As the data analyzed in this study has a distribution which the variance is greater than the mean, a GPR has shown very similar results to an NBR. Therefore, a GPR that is much more recommendable to estimate because not only the variance does not need to be compared to the mean but also the model is a good fit for data of underdispersion.