The invention discloses a mechanical arm fractional order iterative learning control method and system with an initial state learning function. The mechanical arm fractional order iterative learning control method with the initial state learning function comprises the steps that firstly, a kinetic model of a mechanical arm system is established, and an expected movement track of the mechanical arm system is preset; secondly, the initial state of the state quantity of the mechanical arm system and system input of the mechanical arm system are initialized, and the actual movement track of the mechanical arm system is worked out according to the kinetic model of the mechanical arm system; thirdly, whether the tracking error between the actual movement track and the expected movement track is equal to zero or not is judged through calculation, if yes, the actual movement track overlaps with the expected movement track, and the process is ended, and if not, the next step is executed; and fourthly, the initial state of the state quantity of the mechanical arm system is corrected according to the initial state of the tracking error and a set initial state learning gain, system input of the mechanical arm system is corrected according to the tracking error, a set input learning gain, and a fractional order, the actual movement track of the mechanical arm system is worked out accordingly, and then the third step is executed.