The study of earthquake and its forecast is a multi-discipline overlapping. Some new enlightenment is given by non-linear scinence such as frentals and chows. In this paper, the generalized energy fractal dimension, the generalized time fractal dimension, and the generalized space fractal dimension for discribing earthquake are presented. The varying pattern of these three generalized fractal dimension in aftershocks of an earthquake is also discussed. In this way it is pointed out that there is a phenomenon in which three generalized fractal dimesions change from decreasing anomaly before earthquake to increasing repeatedly after earthquake. As the characteristics of the 5th earthquake active period, some opinions are put forward.