A magnon-phonon interaction model is built in the two-dimensional double square ferromagnetic system. By using Matsubara Green function theory, we study magnetic excitation of the system, and calculate the magnon dispersion curve on the main symmetric points and lines in the Brillouin zone. The influences of optical phonon and acoustic phonon on the magnetic excitation of the system are compared, and the influences of the parameter change on the magnon softening are also studied. It is concluded that the coupling of the optical phonon and magnon has predominant effect on the magnon softening, especially the longitudinal optical phonon has the greatest effect on the magnon softening, and the effect of nonmagnetic ion on magnon softening is stronger than that of magnetic ion.