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Understanding the runoff response to climate change in the Tibetan Plateau (TP) is critical to water resources management since TP is the "Water Tower of Asia" and is sensitive to climate change. However, previous studies have paid more attention to the changes in annual and monthly runoff. Therefore, the changes in the characteristics of floods and droughts are still unknown, particularly in the Yarlung Zangbo River basin (YRB) in the southern TP. Therefore, this study simulates the runoff in four subbasins in the YRB using the GR4J_SNOW model to depict the characteristics (including frequency, severity, peak, and duration) of floods on a daily scale and those of droughts on a monthly scale. It is done in historical (1979–2014) and future (2049–2084) periods under different climate scenarios (RCP4.5 and RCP8.5), and then the changes in floods and droughts between the two periods are comprehensively compared. The results indicate that the YRB has experienced marginal streamflow change during the historical period. Under future varying climate change scenarios, however, the YRB might become wetter with increasing frequency, volume, and peak of floods, along with decreasing frequency, severity, and duration of droughts. In the upstream YRB, covered by more snow with a drier climate, the flood and drought characteristics appear to be more sensitive to climate change than in the downstream YRB. This study is helpful for a better understanding of the hydrological process in the TP under climate change and for forming sustainable water resource strategies for the surrounding regions of the TP. Plain Language Summary: The Tibetan Plateau (TP) is the Asian water tower, providing water resources to hundreds of millions of people living downstream. The Yarlung Zangbo River basin (YRB), located in the southern part of the TP, has attracted increasing attention because most of the Tibetan people live there and it is the upper stream of the Brahmaputra River. It is not clear how floods and droughts, the two most serious natural disasters, could change under climate change in the YRB. This study simulates the changes in flood and drought characteristics in the YRB in the historical (1979–2014) and future (2049–2084) periods under different climate scenarios (RCP4.5 and RCP8.5). Our results show that the YRB could become wetter with increasing floods and mitigated droughts in the future, despite minor changes in flood and drought characteristics in the historical period. The change could be stronger upstream than downstream. This study can be helpful for long‐term water resource management and planning on the TP. Key Points: The characteristics of floods and droughts in the Yarlung Zangbo River basin (YRB) are comprehensively analyzed in the past and futureThe YRB is expected to become wetter in the future, reflected by increased floods and alleviated droughtsThe flood and drought characteristics in its drier upstream are more sensitive to climate change than those in the humid downstream [ABSTRACT FROM AUTHOR]