The characteristics of accelerating coronal mass ejection (CME) and decelerating CME happening during 1997—2003 are analyzed. Prediction tests are made for geomagnetic disturbance events caused by the gradually accelerating CME-associated interplanetary shock waves and the decelerating CME-associated interplanetary shock waves, which can be identified by interplanetary scintillation (IPS) observation during 1997—2003. New membership functions and new correctional item of onset time of geomagnetic disturbances are respectively constituted for two kinds of CME. The main results are: for the onset time of the geomagnetic disturbance in the accelerating CME, the relative error between the observation,Tobs, and the prediction,Tpre,ΔTpre/Tobs≤10% for 21.86% of all events, ≤30% for 78.13% and ≥50% for only 9.36%; for the decelerating CME, ΔTpre/Tobs≤10% for 25.00% of all events, ≤30% for 84.37% and ≥50% for only 3.13%.These results show that the method has good feasibility for the geomagnetic disturbance predictions.