The Yellow River Basin is an important economic belt and key ecological reservation area in China. In the context of global warming, it is of great significance to project the drought disaster risk for ensuring water security and improving water resources management measures in practice. Based on the five Global Climate Models (GCMs) projections under three scenarios of the Shared Socioeconomic Pathways (SSP) (SSP126, SSP245, SSP585) released in the Sixth Coupled Model Intercomparison Project (CMIP6), this study analyzed the characteristics of meteorological drought in the Yellow River Basin in combination with SPEI indicators over 2015–2100. The result indicated that: (1) The GCMs from CMIP6 after bias correction performed better in reproducing the spatial and temporal variation of precipitation. The precipitation in the Yellow River Basin may exhibit increase trends from 2015 to 2100, especially under the SSP585 scenario. (2) The characteristics of meteorological drought in the Yellow River Basin varied from different combination scenarios. Under the SSP126 scenario, the meteorological drought will gradually intensify from 2040 to 2099, while the drought intensity under SSP245 and SSP585 scenarios will likely be higher than SSP126. (3) The spatial variation of meteorological drought in the Yellow River Basin is heterogeneous and uncertain in different combination scenarios and periods. The drought tendency in the Loess Plateau will increase significantly in the future, and the drought frequency and duration in the main water conservation areas of the Yellow River Basin was projected to increase.