Among the members of biometric identifiers, the palmprint and the palmvein have received significant attention due to their stability, uniqueness, and non-intrusiveness. In this paper, we investigate the problem of palmprint/palmvein recognition and propose a Deep Convolutional Neural Network (DCNN) based scheme, namely PalmR CNN (short for palmprint/palmvein recognition using CNNs). The effectiveness and efficiency of PalmR CNN have been verified through extensive experiments conducted on benchmark datasets. In addition, though substantial effort has been devoted to palmvein recognition, it is still quite difficult for the researchers to know the potential discriminating capability of the contactless palmvein. One of the root reasons is that a large-scale and publicly available dataset comprising high-quality, contactless palmvein images is still lacking. To this end, a user-friendly acquisition device for collecting high quality contactless palmvein images is at first designed and developed in this work. Then, a large-scale palmvein image dataset is established, comprising 12,000 images acquired from 600 different palms in two separate collection sessions. The collected dataset now is publicly available.