Strain amplitude (SA) dependence of internal friction (IF) in a Cu–Al–Mn shape memory alloy (SMA) is investigated. Microstructure observation is conducted with the aim to clarify related mechanisms. It is found that the IF measured during the continuous heating process shows a nonmonotonous dependence on SA, that is, the IF increases first and then decreases. The increase of IF can be attributed to the mergence of martensite laths promoted by the reorientation of martensite variants, whereas the decrease of IF is related to the decrease in the density of moveable interfaces. The isothermal IF measured at low temperatures increases monotonously with the increase in SA, because the density of movable interfaces and the sliding distance of these interfaces in the tangential direction increase. Thermal cycles can significantly improve the isothermal IF because of the annihilation of quenched‐in vacancies and the reorientation of martensite variants. At around 240 °C, the isothermal IF in all specimens shows a nonmonotonous dependence on SA, which can be ascribed to the dragging effect of quenched‐in vacancies on dislocations and the breakaway of dislocations from these vacancies when the SA is high enough.