Vein biometrics is a high security and privacy preserving identification technology that has attracted increasing attention over the last decade. Deep neural networks (DNNs), such as convolutional neural networks (CNN), have shown strong capabilities for robust feature representation, and have achieved, as a result, state-of-the-art performance on various vision tasks. Inspired by their success, deep learning models have been widely investigated for vein recognition and have shown significant improvement of identification accuracy compared to handcrafted models. Existing deep learning models, however, are vulnerable to adversarial perturbation attacks, where thoughtfully crafted small perturbations can cause misclassification of legitimate images, degrading, thereby, the efficiency of vein recognition systems. To address this problem, we propose, in this paper, VeinGuard, a novel defense framework to defend deep learning classifiers against adversarial palm-vein image attacks, composed of a local transformer-based GAN and a purifier. VeinGuard comprises two components: a local transformer-based GAN (LTGAN) that learns the distribution of unperturbed vein images and generates high-quality palm-vein images, and a purifier consisting of a trainable residual network and of a pre-trained generator from LTGAN that automatically removes a wide variety of adversarial perturbations. The resulting clean images are fed to vein classifiers for identification, thereby avoiding adversarial attacks. We evaluate VeinGuard on three public vein datasets in terms of white-box attacks, black-box attacks, ablation experiments, and computation time. The experimental results show that VeinGuard allows filtering the perturbations and enables the classifiers to achieve state-of-the-art recognition results for different adversarial attacks.