A total of 163 tropical cyclones (TCs) occurred in the eastern China seas during 1979-2011 with four types of tracks: left turning, right turning, straight moving, and irregular. The left-turning type is unusual and hard to predict. In this paper, 133 TCs from the first three types have been investigated. A generalized beta-advection model (GBAM) is derived by decomposing a meteorological field into climatic and anomalous components. The ability of the GBAM to predict tracks 1-2 days in advance is compared with three classical betaadvection models (BAMs). For both normal and unusual tracks, the GBAM apparently outperformed the BAMs. The GBAM's ability to predict unusual TC tracks is particularly encouraging, while the BAMs have no ability to predict the left-turning and right-turning TC tracks. The GBAM was also used to understand unusual TC tracks because it can be separated into two forms: a climatic-flow BAM (CBAM) and an anomalous-flow BAM (ABAM). In the CBAM a TC vortex is steered by the large-scale climatic background flow, while in the ABAM, a TC vortex interacts with the surrounding anomalous flows. This decomposition approach can be used to examine the climatic and anomalous flows separately. It is found that neither the climatic nor the anomalous flow alone can explain unusual tracks. Sensitivity experiments show that two anomalous highs as well as a nearby TC played the major roles in the unusual left turn of Typhoon Aere (2004). This study demonstrates that a simple model can work well if key factors are properly included.