We propose a new discriminant analysis method for high-dimensional data, called High-Dimensional Discriminant Analysis (HDDA). Our approach is based on the assumption that high-dimensional data live in different subspaces with low dimensionality. We therefore propose a new parameterization of the Gaussian model which combines the ideas of dimension reduction and constraints on the model. This parameterization takes into account the specific subspace and the intrinsic dimension of each class to limit the number of parameters to estimate. In addition, it is possible to make additional assumptions on the model to further limit the number of parameters. Our experiments on artificial and real datasets highlight that HDDA is more efficient than classical methods in high-dimensional spaces and with small learning datasets.