The capability of Mn-Cu damping alloy in suppressing stick-slip oscillation when used as the friction pair material is investigated through the experimental method and the forged steel, cast iron, Al alloy and Mn-Cu alloy are chosen for the comparative study. The results show that the Mn-Cu damping alloy and Al alloy have a great potential in suppressing stick-slip oscillation as compared with others. The results also reveal the varying wear behaviours and the relationship between the wear state and the stick-slip oscillation. They indicate that the wear debris on the contact interface make a noticeable contribution to reduce stick-slip oscillation. In addition, the high damping capacity of the Mn-Cu damping alloy may also help to suppress the stick-slip oscillation.