Title: A multi-domain splitting framework for time-varying graph structure. Abstract: The Graph Signal Processing (GSP) methods are widely used to solve structured data analysis problems, assuming that the data structure is fixed. In the recent GSP community, anomaly detection on datasets with the time-varying structure is an open challenge. To address the anomaly detection problem for datasets with a spatial-temporal structure, in this work, we propose a novel graph multi-domain splitting framework, called GMDS, by integrating the time, vertex, and frequency features to locate the anomalies. Firstly, by introducing the discrete wavelet transform into vertex function, we design a splitting approach for separating the graph sequences into several sub-sequences adaptively. Then, we specifically design an adjacency function in the vertex domain to generate the adjacency matrix adaptively. At last, by utilizing the learned graphs to the spectral graph wavelet transform, we design a module to extract vertices features in the frequency domain. To validate the effectiveness of our framework, we apply GMDS in the anomaly detection of actual traffic flow and urban datasets and compare its performances with acknowledged baselines. The experimental results show that our proposed framework outperforms all the baselines, which distinctly demonstrate the validity of GMDS.