Finger-vein recognition is an increasingly promising biometric identification technology in terms of its high identification accuracy and prominent security performance. The main challenge faced by finger-vein recognition is the low recognition performance caused by segmentation error and local difference. To tackle this challenge, a finger-vein recognition method with modified binary tree (MBT) model is proposed in this paper. MBT model is used to describe the relationship and spatial structure of vein branches quantitatively. Based on the MBT model, four stages including rough selection, model correction, segment matching, and comprehensive judgment are presented to achieve a robust matching for fingervein. Experiments demonstrate that the proposed method can boost the performance of finger-vein recognition that is degraded by segmentation error and local difference. While maintaining low complexity, the proposed method achieves 0.12 % equal error rate in the introduced dataset with 8,100 finger-vein images from 150 participants, which outperforms the state-of-the-art methods.