Audio-visual synchronization aims to determine whether the mouth movements and speech in the video are synchronized. VocaLiST reaches state-of-the-art performance by incorporating multimodal Transformers to model audio-visual interact information. However, it requires high computing resources, making it impractical for real-world applications. This paper proposed an MTDVocaLiST model, which is trained by our proposed multimodal Transformer distillation (MTD) loss. MTD loss enables MTDVocaLiST model to deeply mimic the cross-attention distribution and value-relation in the Transformer of VocaLiST. Additionally, we harness uncertainty weighting to fully exploit the interaction information across all layers. Our proposed method is effective in two aspects: From the distillation method perspective, MTD loss outperforms other strong distillation baselines. From the distilled model's performance perspective: 1) MTDVocaLiST outperforms similar-size SOTA models, SyncNet, and Perfect Match models by 15.65% and 3.35%; 2) MTDVocaLiST reduces the model size of VocaLiST by 83.52%, yet still maintaining similar performance.