With the recent advances in technology, a wide range of systems continues to collect a large amount of data over time and thus generating time series. Detecting anomalies in time series data is an important task in various applications such as e-commerce, cybersecurity, and health care monitoring. However, Time-series Anomaly Detection (TSAD) is very challenging as it requires considering both the temporal dependency and the structural dependency. Recent graph-based approaches have made impressive progress in tackling the challenges of this field. In this survey, we conduct a comprehensive and up-to-date review of Graph-based Time-series Anomaly Detection (G-TSAD). First, we explore the significant potential of graph-based methods in identifying different types of anomalies in time series data. Then, we provide a structured and comprehensive review of the state-of-the-art graph anomaly detection techniques in the context of time series. Finally, we discuss the technical challenges and potential future directions for possible improvements in this research field.