Pumqu is the biggest river in the Qomolangma National Natural Reserve in China. It is one of the headwaters of the river Ganges and is an important international river in southern Tibet Autonomous Region (T.A.R). However, there are a lack of systematic studies on Pumqu’s geochemical properties. In this study, water samples were collected systematically from all the river catchments in different seasons in 2021, the spatiotemporal variations of the geochemical characteristics of the catchments and their controlling factors were studied, and the overall water quality of the river was also evaluated. Overall, the results showed that the water from the Pumqu catchments was slightly alkaline, with an average pH of 8.22. The number of total dissolved solids was comparable to the other rivers on the Tibetan Plateau and showed a similar variation over the year. Affected by the natural geothermal spring water discharge, the values of oxidation reduction potential at some sampling sites were negative in the wet season. Generally, Ca2+ and HCO3− were the dominant ions. Carbonate weathering was the main factor affecting the geochemical features of the studied catchments. The results of correlation analysis showed the influence of rock weathering, glacial meltwater, geothermal water discharge and riverine physicochemical processes on the trace elements. The natural geothermal water discharge was particularly responsible for the elevated Li, which appeared in some of the sampling sites and resulted in relatively high WQI values in the sites. The overall water quality of the Pumqu catchments was excellent. This study provides first-hand information on the overall spatial and temporal span of the physicochemical characteristics and water quality of all the catchments of the river Pumqu, one of the major water systems in the central Himalayas.