This paper provides a new classification method of covariance matrices exploiting the t-Wishart distribution, which generalizes the Wishart distribution. Compared to the Wishart distribution, it is more robust to aberrant covariance matrices and more flexible to distribution mismatch. Following recent developments on this matrix-variate distribution, the proposed classifier is obtained by leveraging the Discriminant Analysis framework and providing original decision rules. The practical interest of our approach is shown thanks to numerical experiments on real data. More precisely, the proposed classifier yields the best results on two standard electroencephalography datasets compared to the best state-of-the-art minimum distanceto-mean (MDM) classifiers.