Automatically predicting gender and age group from biometrics traits is an essential and challenging task in many real-world applications. There are several works about using machine learning methods to identify human gender or age through the face, iris, or fingerprint, but only limited research about using palm vein patterns. Considering the powerful feature representation ability of Convolutional Neural Networks (CNN) and the advantages of palm vein biometrics, this paper introduces a new CNN-based method for gender and age classification based on palm vein images. Experimental results show that the proposed model is able to learn discriminative features from palm vein images for these tasks, achieving state-of-the-art results on the VERA database by using a shallow CNN architecture. Besides, the obtained results suggest the feasibility of further studies on multi-task identification approaches and the reduction of the penetration rate in massive databases.