Multivariate time series forecasting has long received significant attention in real-world applications, such as energy consumption and traffic prediction. While recent methods demonstrate good forecasting abilities, they have three fundamental limitations. (i). <italic>Discrete neural architectures:</italic> Interlacing individually parameterized spatial and temporal blocks to encode rich underlying patterns leads to discontinuous latent state trajectories and higher forecasting numerical errors. (ii). <italic>High complexity:</italic> Discrete approaches complicate models with dedicated designs and redundant parameters, leading to higher computational and memory overheads. (iii). <italic>Reliance on graph priors:</italic> Relying on predefined static graph structures limits their effectiveness and practicability in real-world applications. In this paper, we address all the above limitations by proposing a continuous model to forecast <underline><bold>M</bold></underline>ultivariate <underline><bold>T</bold></underline>ime series with dynamic <underline><bold>G</bold></underline>raph neural <underline><bold>O</bold></underline>rdinary <underline><bold>D</bold></underline>ifferential <underline><bold>E</bold></underline>quations (<monospace>MTGODE</monospace>). Specifically, we first abstract multivariate time series into dynamic graphs with time-evolving node features and unknown graph structures. Then, we design and solve a neural ODE to complement missing graph topologies and unify both spatial and temporal message passing, allowing deeper graph propagation and fine-grained temporal information aggregation to characterize stable and precise latent spatial-temporal dynamics. Our experiments demonstrate the superiorities of <monospace>MTGODE</monospace> from various perspectives on five time series benchmark datasets.