Most of the recent researches have determined that finger-vein identification systems have begun to change their direction from hand-crafted feature extraction to automatic feature extraction methods, such as convolutional neural networks (CNN). Although a few ongoing studies still concern handcrafted features, most of the recent works focus on automatic feature extraction via CNN-based algorithms, which has achieved breakthrough results. However, benchmark databases for finger-vein identification have a limited sample size per individual, which makes it difficult for them to capture the best representations in an individuals finger vein. Additionally, with the rise of spoofing attacks, obtaining the best representation of the finger vein has become even more important. Even though these algorithms adapt transfer learning by using pre-trained ImageNet weights, which create a general image feature space, it may be not the most optimal space for finger-vein identification. From this point of view, this paper firstly aims to use Capsule Network to take advantage of using convolutions with a limited number of samples on four finger-vein benchmark sub-databases. Moreover, it aims to extract finger-vein features that are more definable and rationally augments without using any pre-trained weights. Secondly, it compares the CNN-based equivalent and LeNet-5 models to show how Capsule Network is better at approaching representing features. This capsule-based finger-vein identification approach using 32x32 image resolutions achieves an average 95.5% accuracy on four benchmark sub-databases.