We systematically analyzed the Benioff strain release before 65 earthquakes with M S over 6.0 in China from 1978 to 2003 to investigate the generality of the widely discussed accelerating moment release (AMR) phenomenon before strong and intermediate-strength earthquakes. In this approach, a strong or intermediate-strength earthquake is selected as a ``target earthquake,'' and retrospective analysis of seismic activity before the ``target earthquake'' is performed. Simple searching area (three circular areas with different radius centered at the epicenter of the ``target earthquake'') and unified temporal range (8 years) are taken in the analysis. Justification of whether AMR exists is by both visual inspection and by power-law curve fitting. It is found that more than 3/5 of the earthquakes under consideration exhibit clear pre-shock AMR property, and 1/3 of the events seem to be sensitive to the searching area. AMR behavior shows apparent focal mechanism dependence: 15 out of 17 dip-slip earthquakes with stable moment release characteristics against the changing of searching areas exhibit AMR behavior, while 16 out of 25 strike-slip earthquakes with stable moment release characteristics exhibit AMR behavior.