Graph neural networks have been successfully applied to sleep stage classification, but there are still challenges: (1) How to effectively utilize epoch information of EEG-adjacent channels owing to their different interaction effects. (2) How to extract the most representative features according to confused transitional information in confused stages. (3) How to improve classification accuracy of sleep stages compared with existing models. To address these shortcomings, we propose a multi-layer graph attention network (MGANet). Node-level attention prompts the graph attention convolution and GRU to focus on and differentiate the interaction between channels in the time-frequency domain and the spatial domain, respectively. The multi-head spatial-temporal mechanism balances the channel weights and dynamically adjusts channel features, and a multi-layer graph attention network accurately expresses the spatial sleep information. Moreover, stage-level attention is applied to easily confused sleep stages, which effectively improves the limitations of a graph convolutional network in large-scale graph sleep stages. The experimental results demonstrated classification accuracy; MF1 and Kappa reached 0.825, 0.814, and 0.775 and 0.873, 0.801, and 0.827 for the ISRUC and SHHS datasets, respectively, which showed that MGANet outperformed the state-of-the-art baselines.