A new idea of using a stiffer metallic element, such as copper, to enhance the damping of AZ91 magnesium alloy is successfully attempted. The study focuses on the relationship between the damping capability of the composite with the weight percentage of copper added to the matrix. Results of this study show that addition of about 8.1, 15.5 and 20.6 wt.% of copper increases the overall damping capacity of the AZ91 matrix by 64%, 78% and 107%, respectively. Particular emphasis is placed on rationalizing the increase in damping in terms of the increase in dislocation density and presence of plastic zone at the matrix-particulate interface.