EEG is a kind of strong non-stationary random signal, and its features are usually distributed in the three dimensions of time, frequency and space. However, many current EEG-based automatic sleep staging methods still have difficulty carrying out joint analysis in the time domain, frequency domain and spatial domain at the same time, and these methods are also not easy to adapt to the time-varying characteristics of EEG sleep staging features, which further affects the real-time extraction of sleep staging patterns. To solve these problems, this paper proposes a graph convolutional network model named DynGCN, and the model combines a time-varying adjacency matrix with a parameter evolution mechanism. During the construction process of the adjacency matrix, the model integrates frequency-domain coherence, channel weight information and the δ/θ power ratio gating function, then updates the adjacency matrix dynamically in the time dimension, so that the connection relationship between channels can change with EEG rhythm variations. In the graph convolution feature propagation stage, the model further introduces graph convolution kernel weights that can change according to the current input features, and this design improves the ability of the model to represent the time-varying statistical characteristics inside EEG signals to some extent. Through these two types of dynamic designs, the model can reflect the rhythm feature changes of EEG signals and the changing connection relationships among channels in a more timely way within the time dimension. Experimental results on the Sleep-EDFx dataset show that the proposed DynGCN model performs better than several baseline models in terms of accuracy, macro-average F1 score and Cohen’s Kappa coefficient, and the corresponding results reach 89.1%, 82.4% and 0.841, respectively. In addition, ablation experiments further verify the separate effects of adjacency matrix time modeling and parameter evolution on the overall model performance. Overall, DynGCN provides a feasible method for EEG graph convolution modeling based on dynamic graph structures, and the model also shows relatively good performance and certain application value in automatic sleep staging tasks.