In the present paper the interatomic interaction in iron is calculated from the cohesive energy by means of the Mbius 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.