Sleep staging is the foundation of sleep analysis. Recent studies have attempted to integrate multimodal signals, such as electroencephalogram (EEG) and electrooculogram (EOG), to enhance the sensitivity of models. However, these attempts still face limitations in effectively merging multimodal signals, particularly in capturing the interplay of global and local information during sleep stages simultaneously. To address this issue, we propose a Multi-granularity Sleep Staging Network (MGSleepNet), which integrates two core modules: the Global Feature Integration module (GFI) and the Fine-grained Information Capture module (FIC). The GFI effectively captures the global features of EEG and EOG signals through multi-scale convolution, channel attention mechanisms, and spatial attention mechanisms. The FIC module obtains fine-grained interaction information between EEG and EOG by segmenting time periods and employing cross-attention mechanisms. The combination of these modules resulted in an accuracy of 83.16% and 82.46% in five-fold cross-validation across subjects on the Sleep-edf-20 and Sleep-edf-78 datasets, respectively. In addition, we also achieved better than opportunity level performance on our own data sets. Finally, the ablation studies confirmed the benefits of integrating global and fine-grained relevance paradigms to enhance sleep staging performance. The model input research indicated that MGSleepNet demonstrates good performance in sleep staging outcomes.