Abstract: In this paper,a kind of failure diagnosis method for large system based on iteration of function space in dynamic programming is proposed. First ,a new concept about minimum of coefficient product of routes from source state to target state is put for thand an algorithm is given in order to track down this minimum as well as correspondent route. Then,the algorithm is changed into at abular iteration method which is simpler,more regular and helpful for programming. Third,this concept and this algorithm are applied to failure diagnosis of system and steps of diagnosis are detailed. In the end of this paper,this method is shown to be more effective and simpler by simula tionofa pump system failure diagnosis.