Asynchronization issue caused by different types of modalities is one of the major problems in audio visual speech recognition (AVSR) research. However, most AVSR systems merely rely on up sampling of video or down sampling of audio to align audio and visual features, assuming that the feature sequences are aligned frame-by-frame. These pre-processing steps oversimplify the asynchrony relation between acoustic signal and lip motion, lacking flexibility and impairing the performance of the system. Although there are systems modeling the asynchrony between the modalities, sometimes they fail to align speech and video precisely in some even all noise conditions. In this paper, we propose a mutual feature alignment method for AVSR which can make full use of cross modility information to address the asynchronization issue by introducing Mutual Iterative Attention (MIA) mechanism. Our method can automatically learn an alignment in a mutual way by performing mutual attention iteratively between the audio and visual features, relying on the modified encoder structure of Transformer. Experimental results show that our proposed method obtains absolute improvements up to 20.42% over the audio modality alone depending upon the signal-to-noise-ratio (SNR) level. Better recognition performance can also be achieved comparing with the traditional feature concatenation method under both clean and noisy conditions. It is expectable that our proposed mutual feature alignment method can be easily generalized to other multimodal tasks with semantically correlated information.