In the process of acquisition of finger vein images, the high attenuation of near-infrared light in biological tissues reduces the contrast between the vein and non-vein areas, resulting in serious noise interference in the collected finger vein images. Accordingly, this paper proposes a stable enhancement method of the venous blood vessel region combining the Weber law and Gabor filtering. Based on the Weber law, the directional Weber differential excitations are established and combined with Gabor filtering organically in this method. Through the multi-scale and multi-directional characteristics of Gabor filtering, the directional excitation capability of WLD (Weber local descriptor) is amplified, and the mutual cooperation between the optimal response of Gabor filtering and the optimal excitation of Weber law is realized. This effectively highlights the venous blood vessel imaging regions and enhances the degraded finger vein images stably. The experimental results show that the method proposed in this paper has a good image enhancement effect and can effectively improve the distinguishability of the finger vein network.