In this paper, we propose a new discriminative dictionary learning method based on Riemann geometric perception for polarimetric synthetic aperture radar (PolSAR) image classification. We made an optimization model for geometry-aware discrimination dictionary learning in which the dictionary learning (GADDL) is generalized from Euclidian space to Riemannian manifolds, and dictionary atoms are composed of manifold data. An efficient optimization algorithm based on an alternating direction multiplier method was developed to solve the model. Experiments were implemented on three public datasets: Flevoland-1989, San Francisco and Flevoland-1991. The experimental results show that the proposed method learned a discriminative dictionary with accuracies better those of comparative methods. The convergence of the model and the robustness of the initial dictionary were also verified through experiments.