Audio-visual speech recognition (AVSR) attracts a surge of research interest recently by leveraging multimodal signals to understand human speech. Mainstream approaches addressing this task have developed sophisticated architectures and techniques for multi-modality fusion and representation learning. However, the natural heterogeneity of different modalities causes distribution gap between their representations, making it challenging to fuse them. In this paper, we aim to learn the shared representations across modalities to bridge their gap. Different from existing similar methods on other multimodal tasks like sentiment analysis, we focus on the temporal contextual dependencies considering the sequence-to-sequence task setting of AVSR. In particular, we propose an adversarial network to refine frame-level modality-invariant representations (MIR-GAN), which captures the commonality across modalities to ease the subsequent multimodal fusion process. Extensive experiments on public benchmarks LRS3 and LRS2 show that our approach outperforms the state-of-the-arts.