Abstract: In order to improve the robustness of spectral correspondence algorithm for noise and outlier, a structural descriptor based on spectral graph theory is proposed, and the matching objective function combined with geometric consistency is given as well as its solving algorithm.Firstly, a structural descriptor is proposed by utilizing the statistic of graph spectra and spectral gap, consequently the attribute representation of feature point with fixed length is obtained.Secondly, an objective function is defined by combining geometric consistency represented by neighborhood relationship, and then the matching problem is formulated as an optimization problem with one-to-one correspondence constraints.Finally, the solution to the defined objective function is given by using probabilistic relaxation.Comparative experiments applied to both synthetic data and real-world images validate that our method can achieve higher matching accuracy.