We propose new additive boosting models, where the components are copula-based regression models (Noh et al. 2013), and designed such that the model may capture potentially complex interaction effects. The models do not require discretization of continuous covariates, and are therefore suitable for problems with many such covariates. We propose a fitting algorithm based on efficient procedures for model selection and evaluation of model components, which might be used for designing more effective model selection and fitting algorithms for other types of copula based regression models. Software is provided in the R-package copulaboost. Through a simulation study and illustrations on data, we show that the method’s predictive performance is either better than or comparable to the other equivalent methods.