In recent years, finger vein recognition has become more attractive due to some obvious advantages, such as: in-vivo recognition, high anti-counterfeiting, high acceptability, and high stability, etc. But for some finger vein image, its vein structure is too simple and the useful information is too less, the conventional recognition method often behave badly for this kind of image. For this kind of problem, the multi-scale analysis represented by wavelet is a viable choice, which can extract more information from multi scale of finger vein image. However, there is also a main disadvantage for wavelet: the singularity information extracted using wavelet is point singularity, and the representation based on wavelet has too much redundancy. Therefore, the newer and better method is introduced for finger vein recognition: multi-scale geometric analysis (MGA). In this paper, DSST (Discrete Separable Shearlet Transform) is chosen as the image decomposition and feature extraction tool, which is a fast implementation of shearlet and has a better performance than other MGA method. Several kinds of feature extraction method are proposed based on DSST decomposition sub-band for finger vein recognition: Kurtosis value, energy value and Hu invariant moment. In contrast experiment, the method based on MHD (Modified Hausdorff Distance) feature, relative distance feature, template feature, wavelet feature, ridgelet feature and curvelet feature is used for recognition comparison. The experiment result show that the feature extraction method based on DSST is more applicable for finger vein image, and the feature extracted based on DSST has a better performance.