A composite was fabricated by an infiltration process using graphite particulates for damping enhancement phase and a Cu-11.9Al-2.5Mn (wt%) shape memory alloy as the matrix, and the internal friction of the resulting composite was studied. Two internal friction peaks were observed in the quenched specimens during heating at 240℃ and 370℃ respectively, of which only the evolvement and the mechanism of the low-temperature peak were investigated in the present study. It was found that, the peak only appears in the composite; the location of the peak is independent of frequency but its height increases with increasing frequency; the peak rises and shifts towards high temperature as the heating rate is increased; the height increases with increasing volume fraction of the graphite particulates; and it disappears after several thermal cycles. It is demonstrated from these features together with microstructure examinations that the peak results from the interaction between the applied stress and the dislocations in the matrix.