Symmetric positive defined (SPD) matrix has attracted increasing research focus in image/video analysis, which merits in capturing the Riemannian geometry in its structured 2D feature representation. However, computation in the vector space on SPD matrices cannot capture the geometric properties, which corrupts the classification performance. To this end, Riemannian based deep network has become a promising solution for SPD matrix classification, because of its excellence in performing non-linear learning over SPD matrix. Besides, Riemannian metric learning typically adopts a kNN classifier that cannot be extended to large-scale datasets, which limits its application in many time-efficient scenarios. In this paper, we propose a Bag-of-Matrix-Summarization (BoMS) method to be combined with Riemannian network, which handles the above issues towards highly efficient and scalable SPD feature representation. Our key innovation lies in the idea of summarizing data in a Riemannian geometric space instead of the vector space. First, the whole training set is compressed with a small number of matrix features to ensure high scalability. Second, given such a compressed set, a constant-length vector representation is extracted by efficiently measuring the distribution variations between the summarized data and the latent feature of the Riemannian network. Finally, the proposed BoMS descriptor is integrated into the Riemannian network, upon which the whole framework is end-to-end trained via matrix back-propagation. Experiments on four different classification tasks demonstrate the superior performance of the proposed method over the state-of-the-art methods.