Multivariate time series prediction has aroused widely research interests during decades. However, the spatial heterogeneity and temporal evolution characteristics bring much challenges for high-dimensional time series prediction. In this paper, a novel adaptive graph convolution module is introduced to automatically learn the spatial correlation of multivariate time series and a Koopman-based neural differential equation is proposed to simulate the nonlinear system state evolution. In detail, the correlation between multivariate time series is revealed by the consine similarity of node embedding to infer the potential relationship between nodes and the spatio-temporal feature fusion module is utilized. The LSTM-based network is adopted as Koopman operator to reveal the latent states of spatio-temporal time series and the reversible assumption is imposed on the Koopman operator. Furthermore, the Euler-trapezoidal integration are utilized to simulate the temporal dynamics and multiple-step prediction is carried out in the latent space from the perspective of dynamical differential equation. The proposed model could explicitly discover the spatial correlation by adaptive graph convolution and reveal the temporal dynamics by neural differential equation, which make the modeling more interpretable. Simulation results show the effectiveness on spatio-temporal dynamic discovery and prediction performance.