Gaussian discriminant analysis is a popular classification model, that in the precise case can produce unreliable predictions in case of high uncertainty. While imprecise probability theory offer a nice theoretical framework to solve this issue, it has not been yet applied to Gaussian discriminant analysis. This work remedies this, by proposing a new Gaussian discrimi-nant analysis based on robust Bayesian analysis and near-ignorance priors. The model delivers cautious predictions, in form of set-valued class, in case of limited or imperfect available information. Experiments show that including an imprecise component in the Gaussian discriminant analysis produces reasonably cautious predictions, in the sense that the number of set-valued predictions is not too high, and that those predictions correspond to hard-to-classify instances, that is instances for which the precise classifier accuracy drops.