The fate which Greek Tragedy implicts is very important to appreciate and anylse Greek Tragedy.The fate is regarded as objective or abstractive force determing everyting at first,however,with the increasing of knowledge,it enlarges its own apprehension and formulates different concepts such as principle,disposition,justice,or freedom,which interpret natural and social phenomenon.Similiarly,the category of arche that express what makes up the universe has correspondingly changed.In Socrates’era,philosophers reasearch the soul or the spirit instead of arche,and they think that the soul contains the principle of everyting ,and before recognizing world we must recognize ourslves .So , Straightening out the fate and the arche of the evolutive process makes the relationship betweent the two clear,which is also the significant job of this article.