Biometric identification systems play an essential role in multiple application areas, such as banking services, e-government, and public security, among others. Particularly, palm vein recognition is considered an emerging technology from the last decade, avoiding forgery possibilities and presenting high identification reliability and accuracy. State-of-the-art in palm vein recognition has improved its results in recent years from different approaches based on deep learning. Some methods based on convolutional neural networks reported in the literature have achieved high recognition rates in public databases. However, computational simplicity and generalization capability are limited given the small number of samples in the databases. This paper introduces a model called PVEIN-MLELM based on the Multilayer Extreme Learning Machine (ML-ELM) for identifying persons through palm vein images. The ML-ELM algorithm offers advantages in terms of computational simplicity and speed of the training process while maintaining its generalization capability. Experimental results on four public datasets show recognition rates comparable to the state-of-the-art approaches while reducing memory requirements and significantly speeding up computational time.