On-line detection of anomalies in time series is a key technique in various event-sensitive scenarios such as robotic system monitoring, smart sensor networks and data center security. However, the increasing diversity of data sources and demands are making this task more challenging than ever. First, the rapid increase of unlabeled data makes supervised learning no longer suitable in many cases. Second, a great portion of time series have complex seasonality features. Third, on-line anomaly detection needs to be fast and reliable. In view of this, we in this paper adopt an unsupervised prediction-driven approach on the basis of a backbone model combining a series decomposition part and an inference part. We then propose a novel metric, Local Trend Inconsistency (LTI), along with a detection algorithm that efficiently computes LTI chronologically along the series and marks each data point with a score indicating its probability of being anomalous. We experimentally evaluated our algorithm on datasets from UCI public repository and a production environment. The result shows that our scheme outperforms several representative anomaly detection algorithms in Area Under Curve (AUC) metric with decent time efficiency.