In this paper, we propose a novel quality assessment of finger-vein images for quality control in the enrollment and authentication of a finger-vein verification system. First, a Radon transform based model is employed to assess the quality of a finger-vein grayscale image. Second, to assess the quality of a finger-vein binary image, we further proposed three evaluation functions to measure the connectivity, smoothness and reliability of the binary version of the finger-vein image. Finally, the scores from the finer-vein binary images are fused with these from finger-vein grayscale images to improve the performance. Experimental results show that our approach can effectively identify the low quality finger-vein images, which is also helpful in improving the performance of the finger-vein verification system. We also show that instead of choosing the images with the highest quality as the enrollment templates, using the templates with the mid-range quality would achieve better performance with respect to improvement of varication accuracy.