A Nd∶LiYF(Nd∶LYF) laser actively Q-switched with an electrooptic La3Ga5SiO14 (LGS) single crystal was designed. Each end of the Nd∶LiYF rod was cut at Brewster′s angle and the orientation of the two surfaces with respect to the crystal′s optic axis was such as to ensure operation at 1.053 μm, which saved the use of a polarizer. LGS Q-switch has the advantages of small insertion loss (2%), high damage threshold (950 MW/cm2) and non-deliquescence. When the pump energy was 120 J and the repetition rate was 3 Hz, the energy of single pulse was 275 mJ, pulse width was 8 ns, dynamic to static ratio was 76%, pulse fluctuation was smaller than 3%, polarization degree was more than 99%, and beam divergence was 0.7 mrad. The polarization characteristics of the laser, the design of the unstable cavity, the characteristics of the thermal effect of LiYF and its compensation were discussed. The principle, characteristics and problems of the LGS E-O Q-switch were also investigated.