The time series of displacement measured in-situ of landslide is regarded as the unstable random process in the paper. The short-term abnormalities are extracted by means of the homomorphic model and the identification criterion of abnormalities and computing formula of order degree are given. The critical-sliding abnormalities are extracted with one degree difference equation for high pass filter. The prediction is conducted with the grey catastrophe model through the abrupt date set composed of abnormality times .