Effects of different heat treatments on microstructure and damping capacity of Cu-55%Mn alloy were investigated to find an optimum heat treatment condition for a maximum damping capacity. The alloy showed the high level of damping capacity in case of the aging at 375 and 400℃. This is ascribed to the FCC→FCT martensitic transformation and microstructural changes from mottled to tweed band type. The damping capacity had a maximum value of 0.33 in logarithmic decrement when the alloy was aged at 375℃ for 14 hours followed by 20 times of thermal cycling between room temperature and 250℃. The refinement of tweed structure by thermal cycling is thought to be responsible for the highest damping capacity.