In order to deeply analyze the hydrological characteristics and the mechanism of runoff generation and concentration in the Niyang River catchment in Southeast Tibet, the precipitation-runoff water balance problem is examined. Based on meteorological and hydrological observation data, such as daily precipitation and flow, at Gongbujiangda, Baheqiao, Gengzhang hydrological stations etc. in the Niyang River catchment, the phenomenon of watershed average precipitation calculated with the traditional Thiessen polygons method being less than the runoff is analyzed. The precipitation-runoff water imbalance problem is described. The method and steps for distributed computing of the watershed average precipitation for the Niyang River catchment considering the topographical features, spatial distribution regularity of precipitation, and distribution of hydrological stations are proposed, and an example calculation is given. The results show that misunderstanding of the spatial distribution of precipitation in the Niyang River catchment and the calculation of watershed average precipitation with the traditional Thiessen polygons method are the main causes of the water imbalance problem. The calculation of the watershed average precipitation should consider the vertical distribution differences of precipitation in the Niyang River catchment.