In this paper,the multi fractal statistical characteristics of earthquake distribution are summarized.The calculation method of earthquake multi fractal features are presented and the possibility of its application in earthquake prediction research is studied.The fixed radius algorithum,the fixed mass algorithum,and the generalized Grassberger Procaccia algorithum are used to calculate generalized dimension spectrum of earthquake spatial distribution multi fractal from the seismological record data in typical earthquake region in order to catch out the sensitive sighs of strong earthquake occourance.The above three methods are compared to each other for calculation precission,the demand of data amount,and the adaptable area.The extended G P algorithum is first applied and tested in calculation of the spectra D q of some theoretical models ,e.g.Henon map,random distribution.The effects of the quantity of the data sample and the scaling region determination on the calculation results are analyzed.It is concluded that the scaling radius should be less than 1/4 of the diameter of the considered fractal object in order to avoid boundary effect.The D q～t curves observed from the Eastern China,especially the variations of D q (q<0),show clearly feature of dimensioin reducing before the occurrence of strong earthquakes These results demonstrate that the intermediate term symptoms of the approach of a strong earthquake in some regions can be singled out from the multi fractal dimension spectrum of earthquake distribution.