Assessing the stability of terrestrial water storage (TWS) under drought conditions is critical for the sustainable development of water resources. In this study, we integrated surface temperature (ST), leaf area index (LAI), and precipitation (P) data from five different scenarios (History, SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) of the Coupled Model Intercomparison Project Phase 6 (CMIP6) to develop a standardized temperature vegetation precipitation index (STVPI). The index was then utilized to monitor global drought conditions and investigate the stability of TWS to drought disaster. The results showed that STVPI can not only monitor meteorological drought, but also has a remarkable sensitivity and applicability to drought caused by sparse vegetation. Notably, 21.16% of the global land area will have a drought trend under the SSP1-2.6 scenario, while it will rise to 35.81% under the SSP5-8.5 scenario, which underscored the potential for an expansion of drought-affected regions worldwide as a result of ongoing global warming and escalating emissions. In addition, the results also found that the warm temperate and tropical regions at lower elevations have an advantage in maintaining the stability of TWS. Unfortunately, the stability of TWS to drought will decline in the western Sahara Desert, central China and northern United States in the future, where will face a serious water crisis. The research framework provides an important reference for deeply evaluating and scientifically allocating water resources under climate change.