Microstructures, tensile properties at room temperature and damping capacity of hot-rolled and annealed K1A (Mg-0.6%Zr) wrought alloy were investigated, and the obtained results were compared to those of commercial AZ31 (Mg-3%AI-1%Zn) wrought alloy. The hot-rolled K1A alloy exhibited 116 MPa of yield strength, which is ${sim}3$ times higher than that of K1A alloy in as-cast state. Specific damping index (SDI) of hot-rolled K1A alloy was 10.4%, and annealing treatment at $300^{circ}C$ for f hour led to the remarkable increase in its damping capacity up to 22.5% without noticeable deterioration of tensile properties. The AZ31 alloy showed superior tensile properties to K1A alloy both in hot-rolled and annealed conditions, but its damping capacity was very low compared to that of K1A alloy.