This paper proposes SE-DenseNet-HP, a novel finger vein recognition model that integrates DenseNet with a squeeze-and-excitation (SE)-based channel attention mechanism and a hybrid pooling (HP) mechanism. To distinctively separate the finger vein patterns from their background, original finger vein images are preprocessed using region-of-interest (ROI) extraction, contrast enhancement, median filtering, adaptive thresholding, and morphological operations. The preprocessed images are then fed to SE-DenseNet-HP for robust feature extraction and recognition. The DenseNet-based backbone improves information flow by enhancing feature propagation and encouraging feature reuse through feature map concatenation. The SE module utilizes a channel attention mechanism to emphasize the important features related to finger vein patterns while suppressing less important ones. HP architecture used in the transitional blocks of SE-DenseNet-HP concatenates the average pooling method with a max pooling strategy to preserve both the most discriminative and contextual information. SE-DenseNet-HP achieved recognition accuracy of 99.35% and 93.28% on the good-quality FVUSM and HKPU datasets, respectively, surpassing the performance of existing methodologies. Additionally, it demonstrated better generalization performance on the FVUSM, HKPU, UTFVP, and MMCBNU_6000 datasets, achieving remarkably low equal error rates (EERs) of 0.03%, 1.81%, 0.43%, and 1.80%, respectively.