In the present paper the interatomic interaction in iron is calculated from the cohesive energy by means of the Mbius transform formula.The atomic force const ants are calculated using the calculated potential and then the phonon dispersions.In the calculation it is found that only the two-body potential in the intera ction is insufficient,and the three-body potential also needs to be taken into a ccount.In the later calculation the Slater-Kirkwood type three-body potential is used and the calculated results of the phonon dispersions along three major dir ections [100],[110] and [111] are in good agreement with experiment.