Palm-vein identification has emerged as a research hotspot in high-security authentication, due to the unique vascular texture and its resistance to spoofing. However, the scarcity of high-quality palm-vein image samples often restricts the performance and generalization capabilities of deep learning models. To address this challenge, we propose EC-PVGAN, an adversarial generative data augmentation method that leverages affine-equivariant constraints to synthesize realistic and diverse palm-vein samples while preserving structural fidelity. The EC-PVGAN begins by applying random affine transformations to binary vein masks extracted by a segmentation model. These transformed masks are then fed into a Pix2Pix-based generator to produce augmented samples. The equivariance similarity loss and commutativity loss are designed to establish a linear equivalence between the affine transformation and image synthesis, thereby guiding the generator to produce affine-equivariant images. Experimental results on two palm-vein datasets demonstrate that our proposed EC-PVGAN significantly improves the identification accuracy and equal error rates across eight vein classifiers, outperforming classic data augmentation methods.