Finger-vein quality assessment is an important issue in finger-vein verification systems as spurious and missing features in poor quality images may increase the verification error. Despite recent advances, current solutions depend on domain knowledge and are typically driven by visual inspection. In this work, we propose a deep Neural Network (DNN) for representation learning from binary images to predict vein quality. First, driven by the primary target of biometric quality assessment, i.e. verification error minimization, we assume that low quality images are false rejected finger-vein images in a verification system. Based on this assumption, the low and high quality images are labeled automatically. Second, as image processing approaches such as enhancement and segmentation may produce false features and ignore actual ones thus degrading verification accuracy, we train a DNN on binary images and derive deep features from its last hidden layer for quality assessment. Our experiments on two large public finger-vein databases show that the proposed scheme accurately identifies high and low quality images and significantly outperform existing approaches in terms of the impact on equal error rate (EER) improvement