A new method is proposed in this paper—moving cut data-rescaled range analysis (MC-R/S). Tests on the correlated time series suggest that the MC-R/S can accurately detect the time-instants of abrupt change, and the MC-R/S results almost do not depend on the length of subseries and are less affected by noises. So, MC-R/S is suitable to detecting an abrupt dynamic change in those time series exhibiting correlations, and can very well make up the deficiency of moving detrended fluctuation analysis (MDFA).