A novel composite was fabricated using a Cu-11.9Al-2.5Mn (wt%) shape memory alloy as the matrix and macroscopic graphite particulates as the second phase. The damping behavior of the resultant composite was examined in the present study through internal friction measurements. It was found that the net height of the internal friction peak relating to phase transformation decreased in the composite due to the constraining effect of the particulates, but the internal friction background significantly increased with increasing the volume fraction or decreasing the diameter of the particulates, giving rise to an improved damping capacity particularly at low temperatures. It is proposed that the interface damping, dislocation damping and the intrinsic damping of the matrix and the constraint are predominant in the composite.