In this paper, the electro-optic effect of the crystals was observed and discussed in the terahertz range, and theoretic analysis was implemented on the experiment's feasibility. Three crystals, ZnTe, GaAs and Si were chosen as the experimental group in the research, and the way to use terahertz TDS system properly to measure the spectrum changes of refractive indexes of crystals under voltage 0-200 V with 10 cm distance in terahertz range is demonstrated. According to the measurements, the refractive index of GaAs had obvious changes around 0.0932 in the frequency from 800 GHz to 2 THz, the refractive index of ZnTe has comparatively small changes around 0.015, and the refractive index of Si hardly changes. The results have validated that the refractive indexes of electro-optic crystals ZnTe and GaAs have changed as the intensity of the external electric fields varied appropriately. And that may have potential applications in photoelectric devices in the terahertz range. Both theoretic analysis and experimental results demonstrate the experimental study is reasonable and successful.