Precipitation plays an important role in the global water cycle, in addition to material and energy exchange processes. Therefore, obtaining precipitation data with a high spatial resolution is of great significance. We used a geographically weighted regression (GWR)-based downscaling model to downscale Tropical Rainfall Measuring Mission (TRMM) 3B43 precipitation data over the middle and lower reaches of the Yangtze River Basin (MLRYRB) from a resolution of 0.25° to 1 km on an annual scale, and the downscaled results were calibrated using the geographical differential analysis (GDA) method. At present, either the normalized difference vegetation index (NDVI) or a digital elevation model (DEM) is selected as the environmental variable in the downscaling models. However, studies have shown that the relationship between the NDVI and precipitation gradually weakens when precipitation exceeds a certain threshold. In contrast, the enhanced vegetation index (EVI) overcomes the saturation shortcomings of the NDVI. Therefore, this study investigated the performances of EVI-derived and NDVI-derived downscaling models in downscaling TRMM precipitation data. The results showed that the NDVI performed better than the EVI in the annual downscaling model, possibly because this study used the annual average NDVI, which may have neutralized detrimental saturation effects. Moreover, the accuracy of the downscaling model could be effectively improved after correcting for residuals and calibrating the model with the GDA method. Subsequently, the downscaled rainfall was closer to the actual weather station rainfall observations. Furthermore, the downscaled results were decomposed into fractions to obtain monthly precipitation data, showing that the proposed method by utilizing the GDA method could improve not only the spatial resolution of remote sensing precipitation data, but also the accuracy of data.