Abstract: Addressing the problems of instability in spectral characteristics of graph structure in non-rigid transform,a description of graph structure information based on geometry relation histogram and path similarity is proposed in the paper and a graph matching method is developed based on the spectral method.The algorithm first describes the vertex feature based on graph histogram and initializes the candidate assignment.Then the algorithm measures affinity between two assignments with path similarity.Finally,the algorithm achieves the feature sets assignment through a spectral method.Different from traditional approaches,our approach describes the graph structure by graph histogram and path similarity which is simple and abundant.The experimental results demonstrate that the proposed method can achieve higher matching accuracy especially in the cases with perturbation.