In this paper , we ll introduce a kind of O(F)-LOOP operator , which will lead to a hierarchy of any recursive functions:O(F)=O(F)_n. We've proved that this hierarchy, corresponds to the speed-up theorem , i. e. given any r(x)∈O(F)_i, there is a language having O(F)_i+1 complexity which can be speeded up by r(x), and also there is a r(x) in O(F)_i, so that any language having O(F)_i complexity cannot be speeded up by r(x) . Through this, we can grasp the soul of Speed-up theorem in a more higher level.