Unbalanced geometric structure caused by variations with deformations, rotations and outliers is a critical issue that hinders correspondence establishment between image pairs in existing graph matching methods. To deal with this problem, in this work, we propose a dual calibration mechanism (DCM) for establishing feature points correspondence in graph matching. In specific, we embed two types of calibration modules in the graph matching, which model the correspondence relationship in point and edge respectively. The point calibration module performs unary alignment over points and the edge calibration module performs local structure alignment over edges. By performing the dual calibration, the feature points correspondence between two images with deformations and rotations variations can be obtained. To enhance the robustness of correspondence establishment, the L_{2,p} -norm is employed as the similarity metric in the proposed model, which is a flexible metric due to setting the different p values. Finally, we incorporate the dual calibration and L_{2,p} -norm based similarity metric into the graph matching model which can be optimized by an effective algorithm, and theoretically prove the convergence of the presented algorithm. Experimental results in the variety of graph matching tasks such as deformations, rotations and outliers evidence the competitive performance of the presented DCM model over the state-of-the-art approaches.