Nowadays, the iris has become a major instrument, promising to replace fingerprints in identification. In addition, the iris is also a promising biomarker for non-invasive pre-diagnostic problems. To improve the iris recognition ability, in this study, we propose to use Vision Transformer (ViT) combined with Cross-Entropy Loss and Triplet Loss to support the classification. Different from traditional training methods, we conduct a comparison between the ViT model trained from scratch and the ViT-B/16 model fine-tuned from pre-trained weights. The results show that, in the context of limited training data, the fine-tuned model from ViT-B/16 gives significantly higher performance and converges faster than the model trained from scratch. The system is evaluated on various iris databases, including CASIA-Iris-Thousand, CASIA-Iris-Lamp, and CASIA-Interval, demonstrating good stability and generalization ability. The proposed method achieves classification accuracy ranging over 99%, confirming the effectiveness of combining two loss functions and leveraging features from the pretrained ViT model.