Precipitation on the Tibetan Plateau (TP) showed different spatial changes during 1979-2016, with an increasing trend over the northern Tibetan Plateau (NTP) and a slightly negative trend over the southern Tibetan Plateau (STP). The changes in precipitation moisture sources over the NTP and STP are investigated using the improved Water Accounting Model with an atmospheric reanalysis as well as observational precipitation and evaporation data. The results show the region in the northwest (region NW), ranging from the TP to Europe dominated by the westerlies, provides 38.9% of precipitation moisture for the NTP, and the region in the southeast (region SE), ranging from the TP to the Indian Ocean and Indochina dominated by the Asian monsoons, provides 51.4% of precipitation moisture for the STP. For the precipitation increase over the NTP, the SE and TP are the main contributors, contributing around 35.8% and 51.7% of the increase, respectively. The contributions from the SE and TP to the STP are, however, minor and insignificant. Meanwhile, the NW shows a negative trend of -4.2 ± 2.9mmyr ^-1 decade ^-1 (significant at the 0.01 level), which contributes to the negative precipitation trend over the STP. Results during the wet season indicate that moisture sources from the areas dominated by the Asian monsoons have contributed more precipitated moisture for the NTP, but not for the STP. Further analysis reveals that precipitated moisture originating from the Indian subcontinent has increased for the NTP while it has decreased for the STP during 1979-2016.