Sleep stage recognition is crucial for assessing sleep and diagnosing chronic diseases. Deep learning models, such as Convolutional Neural Networks and Recurrent Neural Networks, are trained using grid data as input, making them not capable of learning relationships in non-Euclidean spaces. Graph-based deep models have been developed to address this issue when investigating the external relationship of electrode signals across different brain regions. However, the models cannot solve problems related to the internal relationships between segments of electrode signals within a specific brain region. In this study, we propose a Pearson correlation-based graph attention network, called PearNet, as a solution to this problem. Graph nodes are generated based on the spatial-temporal features extracted by a hierarchical feature extraction method, and then the graph structure is learned adaptively to build node connections. Based on our experiments on the Sleep-EDF-20 and Sleep-EDF-78 datasets, PearNet performs better than the state-of-the-art baselines.