Visual Speech Recognition (VSR) aims to recognize corresponding text by analyzing visual information from lip movements. Due to the high variability and weak information of lip movements, VSR tasks require effectively utilizing any information from any source and at any level. In this paper, we propose a VSR method based on audio-visual cross-modal alignment, named AlignVSR. The method leverages the audio modality as an auxiliary information source and utilizes the global and local correspondence between the audio and visual modalities to improve visual-to-text inference. Specifically, the method first captures global alignment between video and audio through a cross-modal attention mechanism from video frames to a bank of audio units. Then, based on the temporal correspondence between audio and video, a frame-level local alignment loss is introduced to refine the global alignment, improving the utility of the audio information. Experimental results on the LRS2 and CNVSRC.Single datasets consistently show that AlignVSR outperforms several mainstream VSR methods, demonstrating its superior and robust performance.