Xinjiang, located in the arid region of the northwest, is one of the areas most sensitive to global changes. The Kaidu River Basin, situated in the heart of Xinjiang, is one of the sources of China’s largest inland river—the Tarim River. The Kaidu River not only bears the responsibility for supplying water for industrial use and agricultural production and people’s daily life in the basin, but also plays a crucial role in ecological water supply to the Tarim River. Studying and analyzing the characteristics and trends of meteorological condition in the future under climate change can provide important references and a basis for a deeper understanding of changes in the hydrological process and water resources in the basin. Therefore, this paper selects seven precipitation bias correction methods and four temperature bias correction methods to adjust the precipitation and temperature output data of eight general circulation models of the Sixth Coupled Model Intercomparison Project (CMIP6) within the Kaidu River Basin. The applicability of different bias correction methods in the study area is evaluated, and based on the corrected future meteorological data and calculated extreme meteorological index, the trends of meteorological data (precipitation, temperature) in the future period (2025–2050) under four SSP scenarios (SSP1-2.6, SSP2-4.5, SSP3-7.0, SSP5-8.5) in the Kaidu River Basin are analyzed. The results show that: (1) Different types of bias correction methods have different correction focus and effects; their reflections on evaluation indicators are also different. (2) In the future period (2025–2050), the annual precipitation and average temperature in the Kaidu River Basin are higher than those in the historical period (1975–2014). The average annual temperature shows an upward trend in the future, but the annual precipitation shows a downward trend in the future except for the SSP2-4.5 scenario. (3) Compared with the historical period, the extreme precipitation in the future period under the SSP1-2.6, SSP2-4.5, and SSP5-8.5 scenarios is higher than that in the historical period, and the number of rainless days decreases. In the future, under the SSP1-2.6 and SSP5-8.5 scenarios, the probability of meteorological drought events occurring due to high temperatures in the basin may further increase, while under the SSP2-4.5 scenario, the situation of high temperatures and heavy rain in the basin may continue to increase.