In recent years, finger-vein biometrics has attracted extensive attention due to its potential for accurate and efficient identification. Deep neural networks (DNNs) have proven effective in automatically extracting discriminative features from large collections of finger-vein images, resulting in improving the accuracy and efficiency of finger-vein recognition. However, the DNN-based finger-vein recognition faces challenges. For example, designing network structures and tuning parameters rely on human prior knowledge, which can reduce both the effectiveness and efficiency of the recognition. To address these challenges, we propose GNAS-FV, a Gated recurrent unit-based Neural Architecture Search for Finger-Vein recognition, which automatically searches for the optimal network structure, reducing manual intervention and experience dependency, so as to improve the network performance and generalization ability. Specifically, we first provide a publicly available finger-vein database using commercial sensors to promote the development of finger-vein recognition. Then, a gated recurrent unit (GRU)based neural architecture search approach is designed to automatically generate the network structure for the finger-vein image database. Next, we design a parameter-sharing supernet policy, which significantly reduces the search space and computation costs. Finally, the rigorous experiments are conducted on our finger-vein database and a public finger-vein database, and the experimental results demonstrate that the proposed GNAS-FV outperforms state-of-the-art methods in terms of recognition accuracy and equal error rate.