Global warming has brought about great uncertainty to the temporal and spatial evolution of precipitation in the headwaters of the Three Rivers on Qinghai-Tibet Plateau. The temporal and spatial evolution of precipitation in the headwaters region need to be analyzed in response to climate change. According to observed precipitation data from 1967 to 2019 at three representative stations, namely, Maduo, Dari and Banma in Guoluo Prefecture, a typical region in the headwaters, we investigated comprehensively the temporal and spatial evolution of precipitation from perspective of trend, abrupt change, periodicity and spatial distribution by using Mann-Kendall trend test, R/S analysis, Mann-Kendall abrupt change test, moving average difference detection, wavelet analysis and Kriging interpolation. Results unveiled that the M-K statistic Z value of areal average precipitation from 1967 to 2019 in Guoluo reached 4.96, and the linear tendency rate 4.01 mm/a, showing a significant increasing trend; Hurst index amounted to 0.90, indicating that the trend was strong. Abrupt change occurred in 1980-1981, which raised the interannual areal average precipitation in Guoluo by 55%. A periodic variation of 28 a was detected as the first major period. The spatial contour of areal average precipitation saw a progressive increase from 293 mm in the northwest to 693 mm in the southeast. Moreover, precipitation varied remarkably with elevation. The average precipitation in areas above 4 200 m above sea level was about 370 mm, and areas above 3 500 m above sea level and valley regions around 560 mm. The research findings offer an important scientific basis for accurately analyzing the causes of climate change and the hydrological cycle in the headwaters of the Three Rivers.