Finger vein images are rich in orientation and edge features. Inspired by the edge histogram descriptor proposed in MPEG-7, this paper presents an efficient orientation-based local descriptor, named histogram of salient edge orientation map (HSEOM). HSEOM is based on the fact that human vision is sensitive to edge features for image perception. For a given image, HSEOM first finds oriented edge maps according to predefined orientations using a well-known edge operator and obtains a salient edge orientation map by choosing an orientation with the maximum edge magnitude for each pixel. Then, subhistograms of the salient edge orientation map are generated from the nonoverlapping submaps and concatenated to build the final HSEOM. In the experiment of this paper, eight oriented edge maps were used to generate a salient edge orientation map for HSEOM construction. Experimental results on our available finger vein image database, MMCBNU_6000, show that the performance of HSEOM outperforms that of state-of-the-art orientation-based methods (e.g., Gabor filter, histogram of oriented gradients, and local directional code). Furthermore, the proposed HSEOM has advantages of low feature dimensionality and fast implementation for a real-time finger vein recognition system.