Function programming language with iteration operator is an efficient，useful and practical，high—level programming language with sound theoretical foundation．It can represent recursion and iteration．This paper proved that partial iteration functions which are defined by iteration operators from given iteration functions can compute partial recur-sion functions．It means that any turing computable partial functions can be c6mputed effi-ciently by iteration functions with sound theoretical foundation．In this paper,the authors defined the composition operator，primitive iteration operator，minimization iteration oper-ator and partial iteration functions．Then they proved that partial reeursion functions can be computed by partial iteration functions．