In this study, the detrended fluctuation analysis (DFA) method is used to analyse the drought and flood index (DFI) of the past 531 years in 20 stations over east central China. It is found that the variation of the DFI exhibits long-range correlation. The long-range correlation gradually decreases from northwest to southeast over the studied region. Moreover, the recurrence times of droughts or floods also show long-range correlation. The long-range correlation in the DFI data will disappear if the DFI data are randomly shuffled, which was also found in the recurrence time of the randomly shuffled DFI series for each station. The results show that long-range correlation is an intrinsic property of drought or flood events, which could result in the long-range correlation of the corresponding recurrence times. At present, the prediction skill of droughts/floods in Asian-Australian monsoon region is relatively low, particularly in most of China. The long-range correlation of the DFI provides a theoretical basis for climate predictions of droughts/floods and may help improve model performance by amending the model configuration, in terms of addressing parameterization problems and improving atmosphere–ocean coupling.