Microstructures, tensile properties, and damping capacity of the hot-rolled and annealed K1A (Mg-0.7%Zr) wrought alloy were investigated in comparison with those of a commercial AZ31 (Mg-3%Al-1%Zn-0.2%Mn) wrought alloy. The K1A alloy in hot-rolled state shows 116 and 183MPa of tensile yield strength (sigma(YS)) and ultimate tensile strength (sigma(UTS)), respectively, which are significantly higher than those (40 and 130MPa) of the K1A casting alloy. The hot-rolled K1A alloy exhibits 10.4% of specific damping index (SDI) and subsequent annealing treatment remarkably enhances its SDI up to 19.7% without sacrificing the tensile strength. Although the annealed AZ31 alloy has 3.9% of low SDI, its tensile properties are still higher than those of the K1A alloy.