Covariance matrix learning methods have become popular for many classification tasks owing to their ability to capture interesting structures in non-linear data while respecting the Riemannian geometry of the underlying symmetric positive definite (SPD) manifolds. Several deep learning architectures applied to these matrix learning methods have recently been proposed in classification tasks by learning discriminative Euclidean-based embeddings. In this paper, we propose a new Riemannian-based deep learning network to generate more discriminative features for electroencephalogram (EEG) classification. Our key innovation lies in learning the Riemannian barycenter for each class within a Riemannian geometric space. The proposed model normalizes the distribution of SPD matrices and learns the center of each class to penalize the distances between the matrix and the corresponding class centers. As a result, our framework can further simultaneously reduce the intra-class distances, enlarge the inter-class distances for the learned features, and consistently outperform other state-of-the-art methods on three widely used EEG datasets and the data from our stress-induced experiment in virtual reality. Experimental results demonstrate the superiority of the proposed framework for learning the non-stationary nature of EEG signals due to the robustness of the covariance descriptor and the benefits of considering the barycenters on the Riemannian geometry.