Taiwan's pressing problems of childlessness and aging, as well as the shortage of medical resources, have made telemedicine a potential solution and trend. However, the security of identity verification in telemedicine has yet to be perfected. Finger vein identification has the characteristics of non-contact and in-vivo biometrics, and its advantages of hygiene and high security have attracted much attention in medical-related fields and institutions. The development of Finger Vein Recognition (FVR) for telemedicine will contribute to the safety of the telemedicine industry. This study is divided into two phases: the first phase aims to optimize the Finger Vein Recognition (FVR) technique by using a lightweight CNN Finger Vein Recognition (FVR) model combined with Mini-RoI technique to train our FVeinLite FVR model using two datasets, namely, FV-USM and PLUSVein-FV3, and to train the best model using different epoch values. Our trained model has the advantages of high recognition accuracy, fewer parameters, and faster computation speed than other finger vein techniques. Secondly, we combine the model with a self-made low-cost embedded device and create an API with simulated patient data to create a complete Finger Vein Recognition System for telemedicine.