A magnon-phonon interaction model is applied to two_dimensional insulating ferro magnets. By using Matsubara Green function theory, we have studied the magonon spectrum, and calculated the magnon dispersion curve on the main symmetric point and line in the Brillouin Zone for different parameters of the system. It is con cluded that at the boundary of Brillouin Zone there is a strong broadening in th e magnon linewidth and softening. The influences of longitudinal phonon and tran sverse phonon on the softening and broadening in the magnon linewidth are compar ed, and the influences of the parameters are also illustrated.