Vein biometrics is a high security and privacy preserving identification technology that has received increasing attentions. Although deep neural networks (DNNs), such as convolutional neural network (CNN), have been investigated for vein recognition and achieved a significant improvement in accuracy, they still fail to model long-range pixel dependencies in an image. Moreover, their performance is limited because the one-hot label vector employed for training may ignore the relevance among labels. To address these problems, we propose LE-MSVT, a Label Enhancement based Multi-Scale Vein Transformer for palm-vein recognition in this paper. First, we propose a multi-scale vein transformer (MSVT) to learn robust and multi-scale features, which consists of a convolutional block that captures the local information and a self-attention block that extracts scale dependencies among images with different scales. Second, to capture the relevance among labels, we explore a graph convolutional network based label enhancement (GCNLE) approach to recover the realistic label distribution for vein classification improvement. GCNLE exploits a multi-layer perception to learn an effective label correlation matrix for extracting the relation information between an input image and multiple training images from different classes. The label distribution vector is generated and then combined with the one-hot label to compute a realistic label distribution of the input image. Finally, we apply GCNLE to MSVT to obtain LE-MSVT, which is trained in an end-to-end way to further improve the feature representation capacity of MSVT classifier. We conduct extensive experiments in terms of MSVT performance and LE-MSVT improvements on three public palm-vein databases, and the experimental results show that the resulting MSVT outperforms other vein identification approaches and achieves the best performance among existing approaches, and GCNLE can greatly improve the performance of MSVT among other de...