Dynamic mechanical analysis was used to investigate the damping behavior of a U–Nb shape memory alloy in various states, including water quenched (WQ), aging (AG), and cold rolling (CR). Internal friction peaks in the U–Nb alloy were identified, as well as their sensitivity to microstructure. The effects of amplitudes on internal friction and storage modulus were more pronounced in the WQ and AG samples than in the CR samples. A relaxation peak at 200 K was discovered in the U–Nb alloy, and its intensity decreased with aging, as did the activation energy for the relaxation event. It may be that the interaction between H and twin boundaries became more active as a result of the local concentration of Nb with aging. There are three transformation peaks in the current U–Nb alloy in the WQ and AG states, corresponding to phase transformations of α’’→γ0 and γ0→γ, respectively. The damping behavior of the coarse-grained and fine-grained samples differs only slightly, and grain size (grain boundaries), is not believed to be directly responsible for the difference; instead, twin boundaries as damping sources may dominate the damping behavior of the U–Nb alloy.