It is hard for current time series reconstruction methods to achieve the balance of high-precision time series reconstruction and explanation of the model mechanism. The goal of this paper is to improve the reconstruction accuracy with a well-explained time series model. Thus, we developed a function-based model, the CCTM (Continuous Change Tracker Model) model, that can achieve high precision in time series reconstruction by tracking the time series variation rate. The goal of this paper is to provide a new solution for high-precision time series reconstruction and related applications. To test the reconstruction effects, the model was applied to four types of datasets: normalized difference vegetation index (NDVI), gross primary productivity (GPP), leaf area index (LAI), and MODIS surface reflectance (MSR). Several new observations are as follows. First, the CCTM model is well explained and based on the second-order derivative theorem, which divides the yearly time series into four variation types including uniform variations, decelerated variations, accelerated variations, and short-periodical variations, and each variation type is represented by a designed function. Second, the CCTM model provides much better reconstruction results than the Harmonic model on the NDVI, GPP, MSR, and LAI datasets for the seasonal segment reconstruction. The combined use of the Savitzky–Golay filter and the CCTM model is better than the combinations of the Savitzky–Golay filter with other models. Third, the Harmonic model has the best trend-fitting ability on the yearly time series dataset, with the highest R-Square and the lowest RMSE among the four function fitting models. However, with seasonal piecewise fitting, the four models all achieved high accuracy, and the CCTM performs the best. Fourth, the CCTM model should also be applied to time series image compression, two compression patterns with 24 coefficients and 6 coefficients respectively are proposed. The daily MSR dataset can achieve a compression ratio of 15 by using the 6-coefficients method. Finally, the CCTM model also has the potential to be applied to change detection, trend analysis, and phenology and seasonal characteristics ex-tractions.