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With the growing demand for information security, finger-vein recognition has become widespread. However, the robustness of the recognition process becomes a major problem. When identifying unseen categories with traditional finger-vein recognition systems, a few issues remain, such as recognition interference and low efficiency. This paper proposes a Deep Generalized Label Finger-Vein (DGLFV) model to extract feature maps and achieve high-accuracy recognition. The largest rectangular finger-vein region is extracted through image semantic segmentation and the advanced bidirectional traversing and center diffusion method for the known categories. Then we generalize all the unseen categories actively as Class $C+1$ to reduce interference from unregistered users. Furthermore, an adaptive threshold acquisition algorithm is proposed for Label Receiver Operating Characteristic (LROC), so that the procedures of classification, recognition, and verification are unified. Apart from Shandong University Homologous Multi-modal Traits (SDUMLA-HMT), we have conducted additional experiments on our self-built database, Finger Veins of Signal and Information Processing Laboratory (FV-SIPL). The recognition accuracy of the approach proposed in this paper has reached 99.25% and 99.08% testing on FV-SIPL and SDUMLA-HMT, with a low error rate at 1.481% and 2.228% and little time consumption of 0.157s for a single image, which is better than most state-of-the-art finger-vein recognition methods.