Modelling claim frequency and claim severity are topics of great interest in property-casualty insurance for supporting underwriting, ratemaking, and reserving actuarial decisions. Standard Generalized Linear Models (GLM) frequency–severity models assume a linear relationship between a function of the response variable and the predictors, independence between the claim frequency and severity, and assign full credibility to the data. To overcome some of these restrictions, this paper investigates the predictive performance of Gradient Boosting with decision trees as base learners to model the claim frequency and the claim severity distributions of an auto insurance big dataset and compare it with that obtained using a standard GLM model. The out-of-sample performance measure results show that the predictive performance of the Gradient Boosting Model (GBM) is superior to the standard GLM model in the Poisson claim frequency model. Differently, in the claim severity model, the classical GLM outperformed the Gradient Boosting Model. The findings suggest that gradient boost models can capture the non-linear relation between the response variable and feature variables and their complex interactions and thus are a valuable tool for the insurer in feature engineering and the development of a data-driven approach to risk management and insurance.