Abstract The effect of parameters such as strain amplitude, frequency and temperature on damping capacity of magnesium alloy AZ91D as-cast, solution and aged was investigated. Granato–Lucke model was employed to explain the influences of parameters on damping capacity of magnesium alloy. It is shown that solution treatment decreases the amount of second-phase particles distributing inside grains, weakens the strong pinning on dislocations, and increases the internal friction of AZ91D, while aging reduces the value due to precipitation of second-phase particles. The influence of solution treatment and aging on damping capacity of AZ91D at room temperature is the same as at 100 °C. The damping at 100 °C is greater than that at room temperature because of thermal activation.