Palm vein recognition has relevant advantages in comparison with most traditional biometrics, such as high security and recognition performance. In recent years, CNN-based models for vascular biometrics have improved the state-of-the-art, but they have the disadvantage of requiring a larger number of samples for training. In this context, the generation of synthetic databases is very effective for evaluating the performance of biometric systems. The present study proposes a new perspective of a transfer learning approach for palm vein recognition, evaluating the use of Synthetic-sPVDB and NS-PVDB synthetic databases for pre-training deep learning models and validating their performance on real databases. The proposed methodology comprises two different branches as inputs. Firstly, a synthetic database is used to train a CNN model, and in the second branch, a real database is used to finetune and evaluate the performance of the resulting pre-trained model. For the feature learning process, we implemented two end-to-end CNN architectures based on AlexNet and Resnet32. The experimental results on the most representative public datasets have shown the usefulness of using palm vein synthetic images for transfer learning, outperforming the state-of-the-art results.