Modelling is a key issue to get a fair pricing in insurance. Poisson distribution is the basic model for count data when the assumptions of Poisson process are assured. Since the insurers tend not to state the small claims to get the deductibles and no claim discounts, insurance data has more zeros than expected which makes the contradictions of the Poisson process assumptions that is the equality mean and variance value. However, not to take account excess zeros makes the knowledge deficiency to get the better pricing for the portfolio. In this paper we will compare Poisson Models and Zero Inflated Models which account for this fact for claim frequency data. Also we will review the models in use for count data and also compare Hurdle Models as an alternative to Zero Inflated Models. Our results represent that Hurdle Models are better fit than the other models we compare. We used Akaike’s Information Criteria(AIC) as model selection measures.