We systematically studied the effect of annealing on damping capacity of pre-deformed magnesium alloy and demonstrated the close relationship between damping capacity and twin boundary mobility. The damping capacity of pre-compressed AZ31 alloy can be improved by annealing for short period as a result of increased twin boundary mobility. In contrast, the damping capacity will be deteriorated after prolonged annealing in pre-compressed AZ91 alloy, which is ascribed to the stabilization of twin boundary by significant segregation and precipitation. In addition, we firstly succeeded to distinguish the damping capacity contributed by TB motion from that by dislocation motion in Mg alloys. This study provides the strategy to enhance damping capacity by improving twin boundary mobility after appropriate annealing, the time of which depends on the alloying element concentration.