Contactless biometric technologies such as palm vein recognition have gained more relevance in the present and immediate future due to the COVID-19 pandemic. Since certain soft biometrics like gender and age can generate variations in the visualization of palm vein patterns, these soft traits can reduce the penetration rate on large-scale databases for mass individual recognition. Due to the limited availability of public databases, few works report on the existing approaches to gender and age classification through vein pattern images. Moreover, soft biometric classification commonly faces the problem of imbalanced data class distributions, representing a limitation of the reported approaches. This paper introduces weighted extreme learning machine (W-ELM) models for gender and age classification based on palm vein images to address imbalanced data problems, improving the classification performance. The highlights of our proposal are that it avoids using a feature extraction process and can incorporate a weight matrix in optimizing the ELM model by exploiting the imbalanced nature of the data, which guarantees its application in realistic scenarios. In addition, we evaluate a new class distribution for soft biometrics on the VERA dataset and a new multi-label scheme identifying gender and age simultaneously. The experimental results demonstrate that both evaluated W-ELM models outperform previous existing approaches and a novel CNN-based method in terms of the accuracy and G-mean metrics, achieving accuracies of 98.91% and 99.53% for gender classification on VERA and PolyU, respectively. In more challenging scenarios for age and gender–age classifications on the VERA dataset, the proposed method reaches accuracies of 97.05% and 96.91%, respectively. The multi-label classification results suggest that further studies can be conducted on multi-task ELM for palm vein recognition.