Compound drought and heatwave (CDHW) events have received considerable attention in recent years due to their devastating effects on human society and ecosystem. In this study, we systematically investigated the spatiotemporal changes of CDHW events for historical period (1951-2014) and four future scenarios (2020-2100) (SSP1-2.6, SSP2-4.5, SSP3-7.0, and SSP5-8.5) over global land by using Coupled Model Intercomparison Project Phase 6 (CMIP6) models. The sensitivity of the CDHW events to the changes of maximum air temperature and the climatic water balance variables are also examined. The CDHW is defined by integrating monthly standardized precipitation evapotranspiration index (SPEI) and daily maximum temperatures. The results show that the multi-model ensembles project a strong increasing trend in CDHW characteristics over almost all global lands under SSP2-4.5, SSP3-7.0, and SSP5-8.5. A significant increase in CDHW risk will witness across global land areas for the medium to long term future, if there is not aggressive adaptation and mitigation strategies. The results of sensitivity analysis suggest that higher sensitivity of CDHW events to global warming will occur in the future except SSP1-2.6. Particularly, each 1°C global warming increases the duration of the CDHW events by 3 days in the historical period, but by about 10 days in the future period. Overall, this study improves our understanding in the projection of CDHW events and the impacts of climate drivers to the CDHW events under various future scenarios, which could provide support about the risk assessment, adaptation and mitigation strategies under climate change.