Floods that cause yearly economic losses and casualties have increased in frequency with global warming. Assessing the mortality risks of populations due to flooding is important and necessary for risk management and disaster reduction. Thus, this paper develops a method for assessing global mortality risks due to river flooding. Global historical annual death tolls are first estimated during the historical period 1986-2005 (T0) by using available mortality vulnerability functions of river flooding. Then, the best vulnerability function is selected according to lower root mean square errors (RMSE) and the differences in the multi-year mean (DMYM) values. Next, the adjustment coefficient K c for each country (region) is calculated to use in the revision of the selected vulnerability function. Finally, the mortality risks are estimated based on an adjusted vulnerability function. As a case, the paper assessed and analysed the global mortality risks due to river flooding during 2016-2035 (2030s) and 2046-2065 (2050s) for the combined scenario of the Representative Concentration Pathway 4.5 (RCP4.5) and the Shared Socioeconomic Pathway 2 (SSP2), and the RCP8.5-SSP5 scenario. The results show that the estimation errors of the death tolls in most countries (regions) decrease after adjusting the vulnerability function. Under the current defense capacity and vulnerability level, the average annual death tolls of RCP4.5-SSP2 and RCP8.5-SSP5 in the 2030s will increase by 1.05 times and 0.93 times compared with the historical period. They will increase 1.89 and 2.20 times, respectively for the two scenarios during 2050s. High-risk areas are distributed in the south-eastern Eurasia. © 2021 The Author(s). Published by IOP Publishing Ltd.