In this article the new neural network algorithm for palm vein identification using the triplet loss function is proposed. The neural network model is based on the VGG16 architecture. The similarity learning problem instead of the classification problem is considered. The number of image classes is assumed to be unknown so at the output of the neural network the feature vector is obtained, and then for the pair of palm vein images the distance between them is calculated. Minimization of triplet loss function while training leads to the decrease in distances between the images of the same class, while the distances between the images of different classes increase. The neural network was trained using preprocessed and segmented images from CASIA multi-spectral palmprint image database. The use of segmentation information for palm vein recognition improves the recognition results. Experimental results demonstrate the effectiveness of the proposed method. The value of EER=0.0084 is obtained.