Approximate entropy (ApEn) is valid index which can be used to quantitatively reflect dynamic characteristics and complexity of a time series. The ApEn has been developed to detect an abrupt change in one-dimension time series by sliding a fixed widow, which can be identified with an abrupt dynamic change to some extent, but the sliding ApEn results depend on the window scale, and cannot accurately position the time-instant of an abrupt change. Based on this, a new method is proposed in the present paper, i.e., moving cut data-approximate entropy (MC-ApEn), which can be used to detect an abrupt dynamic change in time series. Tests on model time series indicate that the detection results from the present method show relatively good stability and high accuracy, obviously better than those from the sliding ApEn method and the Mann-Kendall method. The applications in daily precipitation records further verify the validity of the present method.