Finger-vein biometrics has been extensively investigated for personal authentication. One of the open issues in finger-vein verification is the lack of robustness against image quality degradation. Spurious and missing features in poor quality images may degrade the system performance. Despite recent advances in finger-vein quality assessment, current solutions depend on domain knowledge. In this work, we propose a deep Neural Network (DNN) for representation learning to predict image quality using very limited knowledge. Driven by the primary target of biometric quality assessment, i.e. verification error minimization, we assume that low quality images are falsely rejected in a verification system. Based on this assumption, the low and high quality images are labeled automatically. We then train a DNN on the resulting dataset to predict image quality. To further improve DNN's robustness, the finger vein image is divided into various patches, on which a patch-based DNN is trained. The deepest layers associated with the patches form together a complementary and an over-complete representation. Subsequently, the quality of each patch from a testing image is estimated and the quality scores from the image patches are conjointly input to P-SVM to boost quality assessment performance. To the best of our knowledge, this is the first proposed work of deep learning-based quality assessment, not only for finger vein biometrics, but also for other biometrics in general. The experimental results on two public finger-vein databases show that the proposed scheme accurately identifies high and low quality images and significantly outperforms existing approaches in terms of the impact on equal error rate (EER) decrease