In recent years, biometric systems have positioned themselves among the most widely used technologies for people recognition. In this context, palm vein patterns have received the attention of researchers due to their uniqueness, non-intrusion, and reliability. Currently, research on palm vein recognition based on deep learning is still very preliminary, most of the works are based on very deep models by using pre-trained models and transfer learning techniques. In this work, we evaluate end-to-end CNN models for palm vein recognition. The proposed method was implemented on seven public databases of palm vein images and two convolutional neural network architectures were evaluated: SingleNet, the proposed architecture of few convolutional layers, and a deeper architecture based on ResNet32. The experimental results demonstrate the superiority of the SingleNet model, outperforming the state-of-the-art results for the IITI, PUT, and FYO databases, achieving the same results on the Tongji and PolyU datasets, and obtaining a slightly lower performance for the VERA and CASIA databases. Comparing to the state-of-the-art approaches, our proposed method is computationally simpler than those that are based on very deep architectures and others that fuse hand-crafted and CNN extracted features.