Damping properties of the inherent and intrinsic internal friction peaks (IF PT + IF I ) of 7.5, 8.0, 8.5, and 9.0 wt. %) shape memory alloys (SMAs) were investigated by using dynamic mechanical analysis. The Cu-7.5Zn-11Al, Cu-8.0Zn-11Al, and Cu-8.5Zn-11Al SMAs with (IF PT + IF I ) β 3 (L2 1 )→γ 3 (2H) peaks exhibit higher damping capacity than the Cu-7.0Zn-11Al SMA with a (IF PT + IF I ) β 3 (L2 1 )→γ 3 (2H) peak, because the γ 3 martensite phase possesses a 2H type structure with abundant movable twin boundaries, while the β 3 phase possesses an 18R structure with stacking faults. The Cu-9.0Zn-11Al SMA also possesses a (IF PT + IF I ) β 3 (L2 1 )→γ 3 (2H) peak but exhibits low damping capacity because the formation of γ phase precipitates inhibits martensitic transformation. The Cu-8.0Zn-11Al SMA was found to be a promising candidate for practical high-damping applications because of its high (IF PT + IF I ) peak with tan δ > 0.05 around room temperature.