Background Heatwaves are a critical public health problem. There will be an increase in the frequency and severity of heatwaves under changing climate. However, evidence about the impacts of climate change on heatwave-related mortality at a global scale is limited. Methods and findings We collected historical daily time series of mean temperature and mortality for all causes or non-external causes, in periods ranging from January 1, 1984, to December 31, 2015, in 412 communities within 20 countries/regions. We estimated heatwave +/- mortality associations through a two-stage time series design. Current and future daily mean temperature series were projected under four scenarios of greenhouse gas emissions from 1971 +/- 2099, with five general circulation models. We projected excess mortality in relation to heatwaves in the future under each scenario of greenhouse gas emissions, with two assumptions for adaptation (no adaptation and hypothetical adaptation) and three scenarios of population change (high variant, median variant, and low variant). Results show that, if there is no adaptation, heatwave-related excess mortality is expected to increase the most in tropical and subtropical countries/regions (close to the equator), while European countries and the United States will have smaller percent increases in heatwave-related excess mortality. The higher the population variant and the greenhouse gas emissions, the higher the increase of heatwave-related excess mortality in the future. The changes in 2031 +/- 2080 compared with 1971 +/- 2020 range from approximately 2,000% in Colombia to 150% in Moldova under the highest emission scenario and high-variant population scenario, without any adaptation. If we considered hypothetical adaptation to future climate, under high-variant population scenario and all scenarios of greenhouse gas emissions, the heatwave-related excess mortality is expected to still increase across all the countries/regions except Moldova and Japan. However, the increase would be much smaller than the no adaptation scenario. The simple assumptions with respect to adaptation as follows: no adaptation and hypothetical adaptation results in some uncertainties of projections. Conclusions This study provides a comprehensive characterisation of future heatwave-related excess mortality across various regions and under alternative scenarios of greenhouse gas emissions, different assumptions of adaptation, and different scenarios of population change. The projections can help decision makers in planning adaptation and mitigation strategies for climate change.