Claim frequency data in general insurance may not follow the traditional Poisson distribution when there are many zeros. When the number of observed zeros exceeds the number of expected zeros under the Poisson distribution, extra dispersion appears. This paper summarizes several dispersed and zero-inflated count data models, which are used to handle dispersion and excess zeros. We model the insurance claim count data with excess zeros with these models. We use chi-square goodness-of-fit, to test the validity of the assumption of the count data distribution and fit count data regression model with predictors. We compare the fits through AIC and BIC. The generalized Poisson model and Negative binomial model provide a good fit to the data.