Considering atomic anharmonic vibration, the authors have figured out the expression of free energy and relaxation of single-domain ferromagnetic granule in magnetic field. They have discussed the influence of damping parameter and temperature on the relaxation of particle magnetization intensity. As a result, atomic anharmonic vibration will affect the free energy of single-domain ferromagnetic granule, but not the relaxation. In a word, the relaxation should augment with damping parameter. It is less influenced by temperature if damping parameter is on the small side or in midst. And the influence should augment with the damping parameter. If the damping invariability is given, the relaxation should augment when the temperature is lower.