Extreme positive-Indian-Ocean-dipole events cause devastating floods in eastern tropical Africa and severe droughts in Asia; increasing greenhouse gas emissions will make these dipole events about three times more frequent in the twenty-first century. Countries in the southern tropical Indian Ocean region are prone to extensive flooding and droughts in years when the Indian Ocean dipole (IOD) climate cycle is in an extreme positive phase. In these bad years, such as 1961, 1994 and 1997, warm waters appear in the western part of the basin and precipitation increases, whereas in the east cooler waters predominate and precipitation decreases. Here Wenju Cai et al. assess climate model projections in a scenario of high greenhouse gas emissions and find that the frequency of extreme positive IODs is likely to increase from one event approximately every 17.3 years through the twentieth century to one event every 6.3 years during the twenty-first century. The Indian Ocean dipole is a prominent mode of coupled ocean–atmosphere variability1,2,3,4, affecting the lives of millions of people in Indian Ocean rim countries5,6,7,8,9,10,11,12,13,14,15. In its positive phase, sea surface temperatures are lower than normal off the Sumatra–Java coast, but higher in the western tropical Indian Ocean. During the extreme positive-IOD (pIOD) events of 1961, 1994 and 1997, the eastern cooling strengthened and extended westward along the equatorial Indian Ocean through strong reversal of both the mean westerly winds and the associated eastward-flowing upper ocean currents1,2. This created anomalously dry conditions from the eastern to the central Indian Ocean along the Equator and atmospheric convergence farther west, leading to catastrophic floods in eastern tropical African countries13,14 but devastating droughts in eastern Indian Ocean rim countries8,9,10,16,17. Despite these serious consequences, the response of pIOD events to greenhouse warming is unknown. Here, using an ensemble of climate models forced by a scenario of high greenhouse gas emissions (Representative Concentration Pathway 8.5), we project that the frequency of extreme pIOD events will increase by almost a factor of three, from one event every 17.3 years over the twentieth century to one event every 6.3 years over the twenty-first century. We find that a mean state change—with weakening of both equatorial westerly winds and eastward oceanic currents in association with a faster warming in the western than the eastern equatorial Indian Ocean—facilitates more frequent occurrences of wind and oceanic current reversal. This leads to more frequent extreme pIOD events, suggesting an increasing frequency of extreme climate and weather events in regions affected by the pIOD.