The current paper introduces new prior distributions on the zero-mean multivariate Gaussian model, with the aim of applying them to the classification of covariance matrices populations. These new prior distributions are entirely based on the Riemannian geometry of the multi-variate Gaussian model. More precisely, the proposed Riemannian Gaussian distribution has two parameters, the centre of mass \bar{Y} and the dispersion parameter σ. Its density with respect to Riemannian volume is proportional to exp(−d^2 (Y ; \bar{Y})), where d^2 (Y ; \bar{Y}) is the square of Rao's Riemannian distance. We derive its maximum likelihood estimators and propose an experiment on the VisTex database for the classification of texture images.