The microstructure, mechanical properties and damping capacities of Mg-Zn-Y alloys were investigated and compared systematically. The results showed that strength and damping of the alloy were increasing markedly with the increase of the volume fraction of long period stacking ordered (LPSO) phase (8%, 16%, 32%, 64%, respectively) on the whole. The corporate effect of LPSO phase and solid solution atoms was beneficial to the strengths. The Mg-1.36Zn-2.28Y can be classified as high damping metals (Q−1≧0.01) at strain amplitudes surpassing 1×10-3. With increasing of the LPSO phase, the critical strain amplitudes of alloys gradually decreased so that alloys can break away from pinning points more easily, thus, achieving a more superior damping performance. In addition, the strain amplitude-independent damping and strain amplitude-dependent damping of the Mg–Zn–Y alloys both increased. The damping capacities of the alloys cannot be explained by the Granato–Lücke theory exclusively.