Background: In modelling claim frequency in actuary science, a major challenge is the number of zero claims associated with datasets. Aim: This study compares six count regression models on motorcycle insurance data. Methodology: The Akaike Information Criteria (AIC) and the Bayesian Information Criterion (BIC) were used for selecting best models. Results: Result of analysis showed that the Zero-Inflated Poisson (ZIP) with no regressors for the zero component gives the best predictive ability for the data with the least BIC while the classical Negative Binomial model gives the best result for explanatory purpose with the least AIC.