A novel porous Cu–11.7Al–2.49Mn (wt%) shape memory alloy (SMA) was fabricated by sintering-dissolution method. Damping behavior of the resulting specimen was investigated by internal friction (IF) technique through the method of forced vibration. An IF peak arises at around 200 °C during heating. This peak has been ascribed to the reverse martensitic transformation (MT). Heat treatments of solution and quenching have important influences on the IF background and the IF peak due to the changes of microstructures and phase constitution of the matrix. Compared with bulk specimen, the porous specimen has a significantly enhanced IF background and a decreased IF peak. It is suggested that the enhancement of IF background originates from the effect of pores and the production as well as movement of dislocations, while the decrease of IF peak from the existence of multifarious defects around pores.