The interaction between the optical rotation and electro-optic effect has been studied. The express equation of the emitted light intensity under the interaction of the optical rotation and electro-optic effect is given, which is I=1-4B2(Asin2ω-Ccos2ω)2. According to the theoretical equation, the shutdown voltage and polarization plane angle for a Q-switch of La3Ga5SiO14 (LGS) crystal with the size of 8 mm×8 mm×25 mm for the wavelength of 1064 nm are calculated to be 4995 V and 27.3°, which is validated by the experiment of a voltage-decreased electro-optical Q-switched Nd∶YAG laser. The experimental results are in basic agreement with the calculation values. The output energy of 361 mJ and the pulse width of 7.8 ns are obtained.