Health risks associated with heatwaves and ozone pollution are projected to rise significantly under the effects of climate change. Although the literature has considered the future health risks of heatwaves and ozone pollution separately, the compound effects remain unexplored, and this could potentially impair risk-prevention plans. Here, using a model from the Coupled Model Intercomparison Project Phase 6 (CMIP6) and four shared socioeconomic pathway (SSPs) scenarios, we explore the global tempo-spatial trend and country disparity of compound-event days and population-exposure person-days. We find that compared with the baseline of 1995-2014, by 2071-2090 under the high-emission scenario of SSP3-7.0, an increased annual mean of 34.6 compound-event days and mean population-exposure of 93.5 million person-days is expected. Furthermore, lower-income countries are facing dramatically higher exposure compared with higher-income countries. These projections could contribute to developing targeted mitigation and adaptation plans.