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Effect of texture on the damping capacity of ZK60 magnesium alloy is investigated through compression experiments with a deformation of 10% at room temperature. It is found that both the dislocation networks, twins and the basal texture intensity affect the damping capacity. At the low strain amplitudes, the dislocation networks and twins are dominant and the damping capacity decreases with the increase in the dislocation networks and twins. At the high strain amplitudes, the basal texture intensity is dominant and the damping capacity decreases with the increase in the basal texture intensity. Based on the anisotropy of the damping capacity of the wrought magnesium alloys, this research provides provide a direction for the study of high-strength and high-damping magnesium alloys.