The grain-boundary relaxation as well as corresponding internal friction (IF) mechanism in Cu-based shape-memory alloy was investigated taking Cu–20.4Al–8.7Mn (at%) as an example. A relaxational IF peak was found at around 214 °C during the heating process, whereas the peak completely disappears during the subsequence cooling process. The IF peak with the activation energy and pre-exponential factor of 1.60 eV and 3.8 × 10−18, respectively, shifting towards higher temperature as the measuring frequency increased indicates that the peak correlates to a thermal-activation process. The results obtained revealed that the viscous sliding of the grain boundaries should be the operative mechanism for the appearance of the peak. However, the appearance of the γ2 precipitate particles formed during the heating process provides a reverse contribution to the peak, leading to the disappearance of the peak due to their pinning effect on the grain boundaries.