The mechanical behaviors and damping capacities of the binary Mg-Ga alloys with the Ga content ranging from 1 to 5 wt.% were investigated by means of optical microscope (OM), scanning electron microscope (SEM), X-ray diffraction (XRD), hardness test, tensile test and dynamic mechanical analyzer (DMA). The hardness (HV_0.5) increases with the increase of Ga content, which can be described as HV_0.5=41.61+10.35c, and the solid solution strengthening effect ？σ_s of the alloy has a linear relationship with cⁿ, where c is the molar fraction of solute atoms and n=1/2 or 2/3. Ga exhibits a stronger solid solution strengthening effect than Al, Zn or Sn due to the large atomic radius difference and the modulus mismatch between Ga and Mg atoms. The addition of Ga makes the Mg-Ga alloys have better damping capacity, and this phenomenon can be explained by the Granato-Lücke dislocation model. The lattice distortion and the modulus mismatch generated because of the addition of Ga increase the resistance to motion of the dislocation in the process of swinging or moving, and thus the better damping capacity is acquired.