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 $400^{circ}C$. This is ascribed to the FCC${ ightarrow}$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 $375^{circ}C$ for 14 hours followed by 20 times of thermal cycling between room temperature and $250^{circ}C$. The refinement of tweed structure by thermal cycling is thought to be responsible for the highest damping capacity.