Satellite-based precipitation products have been widely used to estimate precipitation, especially over regions with sparse rain gauge networks. However, the low spatial resolution of these products has limited their application in localized regions and watersheds. This study investigated a spatial downscaling approach, Geographically Weighted Regression Kriging (GWRK), to downscale the Tropical Rainfall Measuring Mission (TRMM) 3B43 Version 7 over the Lancang River Basin (LRB) for 2001–2015. Downscaling was performed based on the relationships between the TRMM precipitation and the Normalized Difference Vegetation Index (NDVI), the Land Surface Temperature (LST), and the Digital Elevation Model (DEM). Geographical ratio analysis (GRA) was used to calibrate the annual downscaled precipitation data, and the monthly fractions derived from the original TRMM data were used to disaggregate annual downscaled and calibrated precipitation to monthly precipitation at 1 km resolution. The final downscaled precipitation datasets were validated against station-based observed precipitation in 2001–2015. Results showed that: 1) The TRMM 3B43 precipitation was highly accurate with slight overestimation at the basin scale (i.e., CC (correlation coefficient) = 0.91, Bias = 13.3%). Spatially, the accuracies of the upstream and downstream regions were higher than that of the midstream region. 2) The annual downscaled TRMM precipitation data at 1 km spatial resolution obtained by GWRK effectively captured the high spatial variability of precipitation over the LRB. 3) The annual downscaled TRMM precipitation with GRA calibration gave better accuracy compared with the original TRMM dataset. 4) The final downscaled and calibrated precipitation had significantly improved spatial resolution, and agreed well with data from the validated rain gauge stations, i.e., CC = 0.75, RMSE (root mean square error) = 182 mm, MAE (mean absolute error) = 142 mm, and Bias = 0.78% for annual precipitation and CC = 0.95, RMSE = 25 mm, MAE = 16 mm, and Bias = 0.67% for monthly precipitation.