Conformer-based models have proven highly effective in Audio-visual Speech Recognition, integrating auditory and visual inputs to significantly enhance speech recognition accuracy. However, the widely utilized softmax attention mechanism within conformer models encounters scalability issues, with its spatial and temporal complexity escalating quadratically with sequence length. To address these challenges, this paper introduces the Shifted Linear Attention Conformer, an evolved iteration of the conformer architecture. Shifted Linear Attention Conformer adopts shifted linear attention as a scalable alternative to softmax attention. We conducted a thorough analysis of the factors constraining the efficiency of linear attention. To mitigate these issues, we propose the utilization of a straightforward yet potent mapping function and an efficient rank restoration module, enhancing the effectiveness of self-attention while maintaining low computational complexity. Furthermore, we integrate an advanced attention-shifting technique facilitating token manipulation within attentional mechanisms, thereby enhancing information flow across various groups. This three-part approach enhances cognitive computations, particularly beneficial for processing longer sequences. Our model achieves exceptional Word Error Rates of 1.9% and 1.5% on the Lip Reading Sentences 2 and Lip Reading Sentences 3 datasets, respectively, showcasing its state-of-the-art performance in audio-visual speech recognition tasks.