Abstract: A new finger-vein recognition method based on the lightweight Graph Convolutional Network was proposed to solve the problems that the traditional finger-vein recognition methods often had a low accuracy or a huge computational complexity. Before the graph convolution, a finger-vein image was expressed as a weighted graph. The graph’s nodes were decided by the feature of the finger-vein image’s local orientated energy and the correlation between nodes’ feature determined the edges’ weight. As input data, the graph was learned by graph convolution layer defined by Chebyshev polynomial, and fast pooling layer assisted by graph coarsening. Then full connected layers were added to achieve the recognition of finger-vein graph. The experiment results show that the recognition efficiency is much higher than the traditional algorithm and the recognition accuracy is 96.80% in our homemade finger-vein database. Meanwhile, the university of the method is proved in different database.