Establishing correspondence between two given geometrical graph structures is an important problem in computer vision and pattern recognition. In this paper, we propose a robust graph matching (RGM) model to improve the effectiveness and robustness on the matching graphs with deformations, rotations, outliers, and noise. First, we embed the joint geometric transformation into the graph matching model, which performs unary matching over graph nodes and local structure matching over graph edges simultaneously. Then, the L2,1 -norm is used as the similarity metric in the presented RGM to enhance the robustness. Finally, we derive an objective function which can be solved by an effective optimization algorithm, and theoretically prove the convergence of the proposed algorithm. Extensive experiments on various graph matching tasks, such as outliers, rotations, and deformations show that the proposed RGM model achieves competitive performance compared to the existing methods.