Recently cross-channel attention, which better leverages multi-channel signals from microphone array, has shown promising results in the multi-party meeting scenario. Cross-channel attention focuses on either learning global correlations between sequences of different channels or exploiting fine-grained channel-wise information effectively at each time step. Considering the delay of microphone array receiving sound, we propose a multi-frame cross-channel attention, which models cross-channel information between adjacent frames to exploit the complementarity of both frame-wise and channel-wise knowledge. Besides, we also propose a multi-layer convolutional mechanism to fuse the multi-channel output and a channel masking strategy to combat the channel number mismatch problem between training and inference. Experiments on the AliMeeting, a real-world corpus, reveal that our proposed model outperforms single-channel model by 31.7\% and 37.0\% CER reduction on Eval and Test sets. Moreover, with comparable model parameters and training data, our proposed model achieves a new SOTA performance on the AliMeeting corpus, as compared with the top ranking systems in the ICASSP2022 M2MeT challenge, a recently held multi-channel multi-speaker ASR challenge.