Unlike traditional Automatic Speech Recognition (ASR), Audio-Visual Speech Recognition (AVSR) takes audio and visual signals simultaneously to infer the transcription. Recent studies have shown that Large Language Models (LLMs) can be effectively used for Generative Error Correction (GER) in ASR by predicting the best transcription from ASR-generated N-best hypotheses. However, these LLMs lack the ability to simultaneously understand audio and visual, making the GER approach challenging to apply in AVSR. In this work, we propose a novel GER paradigm for AVSR, termed AVGER, that follows the concept of ``listening and seeing again''. Specifically, we first use the powerful AVSR system to read the audio and visual signals to get the N-Best hypotheses, and then use the Q-former-based Multimodal Synchronous Encoder to read the audio and visual information again and convert them into an audio and video compression representation respectively that can be understood by LLM. Afterward, the audio-visual compression representation and the N-Best hypothesis together constitute a Cross-modal Prompt to guide the LLM in producing the best transcription. In addition, we also proposed a Multi-Level Consistency Constraint training criterion, including logits-level, utterance-level and representations-level, to improve the correction accuracy while enhancing the interpretability of audio and visual compression representations. The experimental results on the LRS3 dataset show that our method outperforms current mainstream AVSR systems. The proposed AVGER can reduce the Word Error Rate (WER) by 24% compared to them. Code and models can be found at: https://github.com/CircleRedRain/AVGER.