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At present, ResNet and DenseNet have achieved significant performance gains in the field of finger-vein biometric recognition, which is partially attributed to the dominant design of cross-layer skip connection. In this manner, features from multiple layers can be effectively aggregated to provide sufficient discriminant representation. Nevertheless, an over-dense connection pattern may induce channel expansion of feature maps and excessive memory consumption. To address these issues, we proposed a low memory overhead and fairly lightweight network architecture for finger-vein recognition. The core components of the proposed network are a sequence of sparsified densely connected blocks with symmetric structure. In each block, a novel connection cropping strategy is adopted to balance the channel ratio of input/output feature maps. Beyond this, to facilitate smaller model volume and faster convergence, we substitute the standard convolutional kernels with separable convolutional kernels and introduce a robust loss metric that is defined on the geodesic distance of angular space. Our proposed sparsified densely connected network with separable convolution (hereinafter dubbed ‘SC-SDCN’) has been tested on two benchmark finger-vein datasets, including the Multimedia Lab of Chonbuk National University (MMCBNU)and Finger Vein of Universiti Sains Malaysia (FV-USM), and the advantages of our SC-SDCN can be evident from the experimental results. Specifically, an equal error rate (EER) of 0.01% and an accuracy of 99.98% are obtained on the MMCBNU dataset, and an EER of 0.45% and an accuracy of 99.74% are obtained on the FV-USM dataset.