In this study, the relationship between strength and damping capacity of annealed magnesium alloys after hot rolling was investigated. The microstructure of hot rolled magnesium consisted of dendrite structure and $Mg_{17}Al_{12}$ compounds precipitated along the grain boundary. The dendrite structure was dissipated, $Mg_{17}Al_{12}$ compounds was decomposed by annealing, and then its dissolved in ${alpha}$-Mg. With an increasing the annealing temperature and time, strength was slowly decreased and damping capacity was slowly increased by the growth of grain size and decreasing of defects induced by hot rolling. In annealing treatmented magnesium alloys after hot rolling, damping capacity was decreased rapidly with an increase of strength. There was on proportional relationship between tensile strength, and damping capacity.