Conventional finger-vein recognition systems perform recognition based on the finger-vein lines extracted from the input images or image enhancement, and texture feature extraction from the finger-vein images. In these cases, however, the inaccurate detection of finger-vein lines lowers the recognition accuracy. In the case of texture feature extraction, the developer must experimentally decide on a form of the optimal filter for extraction considering the characteristics of the image database. To address this problem, this research proposes a finger-vein recognition method that is robust to various database types and environmental changes based on the convolutional neural network (CNN). In the experiments using the two finger-vein databases constructed in this research and the SDUMLA-HMT finger-vein database, which is an open database, the method proposed in this research showed a better performance compared to the conventional methods.