Insurance claims are often modelled by a standard Poisson model with fixed effects. With such a model, no individual adjustments are made to account for unobserved heterogeneity between policyholders. A Poisson model with random effects makes it possible to detect policyholders with a high or low individual risk. The premium can then be adjusted accordingly. Others have applied such models without much focus on the model’s prediction performance. As the usefulness of an insurance claims model typically is measured by its ability to predict future claims, we have chosen to focus on this aspect of the model. We model insurance claims with a Poisson random effects model and compare its performance with the standard Poisson fixed effects model. We show that the random effects model both fits the data better and gives better predictions for future claims for high risk policy holders than the standard model.