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Automatic detection of subsequence anomalies (i.e., an abnormal waveform denoted by a sequence of data points) in time series is critical in a wide variety of domains. However, most existing methods for subsequence anomaly detection often require knowing the length and the total number of anomalies in time series. Some methods fail to capture recurrent subsequence anomalies due to using only local or neighborhood information for anomaly detection. To address these limitations, in this paper, we propose a novel graph-represented time series (GraphTS) method for discovering subsequence anomalies. In GraphTS, we provide a new concept of time series graph representation model, which represents both recurrent and rare patterns in a time series. Particularly, in GraphTS, we develop a new 2D time series visualization (2Dviz) method, which compacts all 1D time series patterns into a 2D spatial temporal space. The 2Dviz method transfers time series patterns into a higher-resolution plot for easier sequence anomaly recognition (or detecting subsequence anomalies). Then, a Graph is constructed based on the 2D spatial temporal space of time series to capture recurrent and rare subsequence patterns effectively. The represented Graph also can be used to discover single and recurrent subsequence anomalies with arbitrary lengths. Experimental results demonstrate that the proposed method outperforms the state-of-the-art methods in terms of accuracy and efficiency.