Human wrist vein biometric recognition is one of the least used vascular biometric modalities. Nevertheless, it has similar usability and is as safe as the two most common vascular variants in the commercial and research worlds: hand palm vein and finger vein modalities. Besides, the wrist vein variant, with wider veins, provides a clearer and better visualization and definition of the unique vein patterns. In this paper, a novel vein wrist non-contact system has been designed, implemented, and tested. For this purpose, a new contactless database has been collected with the software algorithm TGS-CVBR®. The database, called UC3M-CV1, consists of 1200 near-infrared contactless images of 100 different users, collected in two separate sessions, from the wrists of 50 subjects (25 females and 25 males). Environmental light conditions for the different subjects and sessions have been not controlled: different daytimes and different places (outdoor/indoor). The software algorithm created for the recognition task is PIS-CVBR®. The results obtained by combining these three elements, TGS-CVBR®, PIS-CVBR®, and UC3M-CV1 dataset, are compared using two other different wrist contact databases, PUT and UC3M (best value of Equal Error Rate (EER) = 0.08%), taken into account and measured the computing time, demonstrating the viability of obtaining a contactless real-time-processing wrist system.