Accurate and timely prediction of power system states is one of the most important challenging tasks in modern power systems. Considering the integration of renewable energy sources, recent deep learning-based models have been well studied and found to have benefits in exploiting spatial–temporal relationships in power system data. However, the complexity of different power system topology structures is not substantially captured since the existing models did not fully consider the graph-based information retrieved from power networks. To resolve the problem, a spatial–temporal attention graph-based network (ST-AGNet), an adaptive power system state prediction approach that utilizes graph-based information data to account various typologies of complex power systems, is proposed. Initially, the power flow model is used for generating historical system state data. With the graph-based topology information, the input dataset with the spatial and temporal features is fed into the proposed network for the training and validating process. Meanwhile, the connectivity of the time-varying graph-based information are accounted in the proposed model. Case studies demonstrate the superiority of the ST-AGNet model over the existing baselines under four different scales of complex systems, which can significantly support dynamic power system analysis and operational tasks.