The left-lateral strike-slip Xianshuihe fault system, located in eastern Tibet, is one of the most tectonically active intracontinental fault systems in China, if not in the world, along which more than 20 M \textgreater6.5 earthquakes have occurred since A.D. 1700, including the 2010 Mw 6.9 Yushu earthquake. It is therefore essential to precisely determine its slip rate, which remains poorly constrained at all time scales, in order to evaluate regional earthquake hazard. Here, we focus on the NW segment of the Xianshuihe fault system, the Ganzi fault. We studied three sites where the active Ganzi fault cuts and left-laterally offsets moraine crests and fan edges. We constrained left-lateral offsets using light detection and ranging (LiDAR) and kinematic global positioning system (GPS) methods, and we used cosmogenic dating to determine the abandonment age of the offset surfaces. We found that the slip rate remains constant along the entire Ganzi fault (similar to 300 km) at 6-8 mm/yr at the late Quaternary time scale, consistent with geodetic (interferometric synthetic aperture radar [InSAR] and GPS) as well as geologic slip rates (4.9-7.5 mm/yr since ca. 12.6 Ma). This implies that the Manigango segment of the Ganzi fault could potentially produce a M 7.6 earthquake in the near future. While the Xianshuihe fault system propagated from west to east, the fact that the Ganzi fault's long-term slip rate is similar to that of the Xianshuihe fault to the SE suggests that the onset of the Xianshuihe fault system at ca. 13 Ma marked a major transition in tectonic regime in SE Tibet.