Palm-vein recognition is gaining significant attention as a high-security biometric recognition technology. However, the vein image acquisition process is easily affected by several factors, making vein texture segmentation a challenging task. Recently, foundation models such as Segment Anything Model (SAM) have shown remarkable potential in image segmentation without requiring prior retraining. Nevertheless, due to the large domain discrepancy between the resource and target domains, as well as limited datasets, existing solutions that rely heavily on abundant training images often struggle to extract robust vein texture patterns. To address this challenge, we propose AdVeinSAM, an adversarial learning-based large model for palm-vein texture extraction, which leverages rich knowledge of large models to enhance vein pattern segmentation. Specifically, by alternately optimizing the vein segmentation model and the image generator, AdVeinSAM generates diverse training samples, effectively transferring knowledge from the large model to enhance feature extraction robustness. First, we incorporate the wavelet transform into xLSTM-UNet to design Wavelet-xLSTM-UNet, which generates diverse and realistic vein images for data augmentation. Then, we improve the NOLA model to fine-tune the segmentation anything model (SAM) and develop a specialized vein segmentation model (VeinSAM), which effectively extracts palm-vein texture features. Finally, the image generator (Wavelet-xLSTM-UNet) and the vein segmentation model (VeinSAM) are combined to form AdVeinSAM, where the generator and the VeinSAM are alternatively updated through adversarial training. Concretely, the image generator generates challenging samples to increase the segmentation difficulty for VeinSAM, while VeinSAM learns more robust feature representations from these challenging samples to improve the generalization and segmentation accuracy. We conduct extensive experiments on three public palm-vein databases and experimental results demonstrate that the proposed AdVeinSAM model outperforms state-of-the-art solutions, achieving the lowest equal error rates (EERs) of 1.48%, 4.76%, and 0.72%, respectively. These results confirm the effectiveness and robustness of AdVeinSAM in palm-vein texture extraction.