Abstract: The global feature representation method of finger-vein based on graph model can not only reduce the dependence of imaging quality on acquisition equipment, but also improve the matching efficiency. Aiming at the problems of unstable graph structure in the current study of finger-vein graph models,that with the matching efficiency decreases as the graph model becomes larger, this paper proposed a method of constructing weighted graph based on SLIC (Simple Linear Iterative Clustering) superpixels segmentation algorithm, and improved ChebyNet Graph convolutional neural networks (GCNs) to extract graph-level features of weighted graph. Because the number of finger-vein samples is generally small, while the number of parameters in ChebyNet are large,it is easy to cause over-fitting and the problem that its fast pooling layer unable to adaptively select the nodes. In this paper, an improved GCNs model SCheby-MgPool (Simplified Cheby-Multi gPool) with global pooling structure was proposed. The experimental results show that the finger-vein features extracted according to the method proposed in this paper have better performance in recognition accuracy and matching efficiency.