Several studies have indicated that glaciers in the Qinghai-Tibet plateau are thinning, resulting in reduced water supplies to major rivers such as the Yangtze, Yellow, Lancang, Indus, Ganges, Brahmaputra in China, and south Asia. Three rivers in the upstream of Yangtze River originate from glaciers around the Geladandong snow mountain group in central Tibet. Here we used elevation observations from Ice, Cloud, and land Elevation Satellite (ICESat) and reference elevations from a 3-arc-second digital elevation model (DEM) of Shuttle Radar Terrestrial Mission (SRTM), assisted with Landsat-7 images, to detect glacier elevation changes in the western (A), central (B), and eastern (C) regions of Geladandong. Robust fitting was used to determine rates of glacier elevation changes in regions with dense ICESat data, whereas a new method called rate averaging was employed to find rates in regions of low data density. The rate of elevation change was -0.158 ± 0.066 ma-1 over 2003-2009 in the entire Geladandong and it was -0.176 ± 0.102 ma-1 over 2003-2008 in Region C (by robust fitting). The rates in Regions A, B, and C were -0.418 ± 0.322 ma-1 (2000-2009), -0.432 ± 0.020 ma-1 (2000-2003), and -0.321 ± 0.139 m-a-1 (2000-2008) (by rate averaging). We used in situ hydroclimatic dataset to assess these negative rates: the glacier thinning was caused by temperature rises around Geladandong, based on the temperature records over 1979-2009, 1957-2013, and 1966-2013 at stations Tuotuohe, Wudaoliang, and Anduo. The thinning Geladandong glaciers led to increased discharges recorded at the river gauge stations Tuotuohe and Chumda over 1956-2012. An unabated Geladandong glacier melting will reduce its long-term water supply to the Yangtze River Basin, causing irreversible socioeconomic consequences and seriously degrading the ecological system of the Yangtze River Basin.