Abstract In this study, we analyze the influences of carbon nanotube (CNT) addition on the martensite transformation and internal friction of Cu–Al–Ni shape-memory alloys (SMAs). X-ray diffraction and differential scanning calorimetry results demonstrate that Cu–13.5Al–4Ni– x CNT ( x  = 0, 0.2, 0.4, 0.6, and 0.8 wt%) SMA/CNT composites exhibit a $${\upbeta }_{1}({\mathrm{DO}}_{3})\rightleftarrows {\upbeta }_{1}^{\mathrm{^{\prime}}}(18\mathrm{R})$$ β 1 ( DO 3 ) ⇄ β 1 ′ ( 18 R ) martensitic transformation. The martensitic transformation temperatures and transformation enthalpies of the martensitic transformation peaks for the Cu–13.5Al–4Ni– x CNT ( x  = 0–0.8 wt%) composites gradually decrease with the increase in the amount of CNT addition. Compared to the Cu–13.5Al–4Ni SMA, the Cu–13.5Al–4Ni– x CNT ( x  = 0.2–0.8 wt%) SMA/CNT composites exhibit significant improvements in the amount of dissipation of energy (storage modulus ( $${E}^{\prime}))$$ E ′ ) ) and mechanical strength. However, the tan δ of the internal friction peak gradually decreases with the increase in the CNT content above 0.6 wt%. The reduction in tan δ is attributed to the decrease in the magnitude of the austenite-to-martensite transformation and precipitation of γ 2 (Cu 9 Al 4 ) phase particles, which impede the interface motion in between the parent/martensitic phase and martensitic phase.