A magnon-phonon interaction model is built in two-dimensional insulating ferromagnet. By using Matsubara Green function theory, we have studied the magnon damping -ImΣ*(1)(k), and calculated the magnon damping -ImΣ*(1)(k) curve on the main symmetric point and line in the Brillouin zone for different parameters of the system. It is concluded that at the boundary of Brillouin zone there is a strong magnon damping. But the magnon damping is very small on zones of small wave vectors, and magnon damping has maximal value at very low temperature. The influences of longitudinal phonon and transverse phonon on the magnon damping are compared, and the influences of the parameters are also illustrated. According to expression -ImΣ*(1)(k)=/(2τ), the magnon lifetime is discussed.