Droughts are among the costliest natural disasters with far-reaching impacts. Focusing on the influence of El Niño–Southern Oscillation (ENSO) on worldwide droughts, this paper presents a formulation of the complex network of concurrent droughts across the Major River Basins (MRBs) of the World. Specifically, concurrent droughts are measured by event synchronization and interconnections of concurrent droughts are determined by significance test. Event coincidence analysis is incorporated into interconnections to quantify the effects of El Niño and La Niña events. A case study is devised for the 3-monthly standardized precipitation index (SPI) of Global Drought and Flood Catalogue during the period from 1950 to 2016. The results highlight that owing to the synchronization of droughts, there exist nine communities of the MRBs, each covering MRBs across different continents. While the correlation between SPI and ENSO exhibits mixed patterns for MRBs grouped by continent, there exist distinct patterns of correlation for MRBs grouped by community. Overall, 28.88% of concurrent droughts tend to be modulated by El Niño events, especially over MRBs in South-West Pacific, South Africa, northern South America and South Asia. In the meantime, 23.51% of concurrent droughts tend to be modulated by La Niña events, especially over MRBs in the United States, southwestern South America, northern China and Central Asia. The modulation of El Niño and La Niña is confirmed by composite analysis of SPI and detailed analysis of the Yangtze River Basin. Overall, the complex network provides useful information for drought forecasting and disaster mitigation.