The use of finger-vein (FV) trait for the purpose of identity authentication has attracted much attention in recent years. However, most of the conventional FV recognition methods are hand-crafted by design and require strong prior knowledge, which are ineffective at expressing the distinctiveness of the FV images. In this paper, we propose an adaptive discriminant and sparsity feature descriptor (DSFD) for FV feature extraction and recognition. Specifically, we first form a direction difference vector (DDV) to better represent the direction feature of the FV images. Afterwards, the DSFD adaptively projects the DDVs into a feature space with discriminative binary codes in which the distance of the within-class samples is minimized and simultaneously the distance of the between-class samples is maximized. Lastly, we concatenate the block-wise histograms into a global histogram as the final feature descriptor for FV recognition. Experimental results on two publicly available FV databases demonstrate the effectiveness of the proposed method.