Hypersonic vehicles experience harsh flight conditions during the reentry phase. Accurate prediction of kinematic states, such as position and attitude angles, is essential to ensure flight safety. Purely data-driven time series prediction methods lack constraints from physical mechanisms during training, which leads to weak model interpretability. Furthermore, cumulative errors often occur in multi-step forecasting. This paper proposes a Physics-Guided Dual-Graph Multiscale Network (PG-DGNet). Physical rules contained in the flight dynamics equations are integrated. Under a graph neural network framework, spatial correlations among state variables and dynamic temporal evolution within each variable are jointly modeled. In addition, a multiscale cascading module is designed. Dilated causal convolutional networks are used to extract hierarchical features. Cumulative errors in multi-step prediction are significantly suppressed. Experimental results show that on the Winged-cone vehicle dataset, PG-DGNet has superior performance compared to models such as LSTM and Transformers. The coefficient of determination R2 for all variable predictions exceeds 95%. Prediction error for key dynamic variables reduces over 50%. This method, through the fusion of physical rules and a multiscale feature architecture, effectively improves hypersonic vehicle multistep prediction accuracy.