Changes in microstructure and damping capacity with aging time for solutionized Mg-Al alloy have been investigated. Discontinuous ${eta};(Mg_{17}Al_{12})$ precipitates form along the primary grain boundaries, the amount of which increases as the aging time increases. The hardness of the matrix with respect to aging time shows a typical "S" shape, indicating a generation of fine continuous precipitates in the matrix during the aging. The peak level of damping capacity is obtained after 1 hour of aging, over which the damping capacity becomes deteriorated continuously. The formation of optimum density of continuous ${eta}$ precipitates with fine morphology which would act as pinning points for dislocation lines, might be responsible for the improvement of damping capacity.