Anomaly detection on multi-dimensional time series is an important research problem in temporal data analysis. In recent years, large-scale industrial time series data have been collected and accumulated by equipment sensors from Industrial Internet of Things (IIoT). These data show the feature of diversity data patterns and workflows, which requires high performance of anomaly detection methods in efficiency, effectiveness, and reliability. Besides, there exists latent correlation between sequences from different dimensions. The correlation information can be used to identify and explain anomalies in data. Based on this, this study proposes a correlation analysis based anomaly detection on multi-dimensional time series data. It first computes correlation values among sequences after standardization steps, and a time series correlation graph model is constructed. Time series cliques are constructed according to correlation degree in the time series correlation graph. Anomaly detection is processed within and out of a clique. Experimental results on a real industrial sensor data set show that the proposed method is effective in anomaly detection tasks in high dimensional time series data. Through contrast experiments, the proposed method is verified to have a better performance than both the statistic-based and the machine learning-based baseline methods. Research in this study achieves reliable correlation knowledge mining between time series, which not only saves time costs, but also identifies abnormal patterns form complex conditions.