In this study, effect of heat treatment on the microstructure and damping capacity of hot rolled magnesium alloys was investigated. The microstructure of hot rolled magnesium consisted of dendrite structure and $Mg_{17}Al_{12}$ compounds precipitated along the grain boundry. The dendrite structure was dissipated and $Mg_{17}Al_{12}$ compounds was decomposed by annealing treatment, and then they dissolved in ${alpha}-Mg$. With an increasing the annealing temperature and time, damping capacity was slowly increased by the growth of grain size and decreasing of defects induced by hot rolling. Two kinds of magnesium alloys AZ 31 and AZ 61 after annealing showed no difference in damping capacity.