The calculation curves of the refractive index and absorption coefficient of ZnTe electro-optic crystal with the frequency of terahertz wave were given, and the phase velocity and group velocity of terahertz wave propagating in ZnTe were compared. Through the electro-optic efficiency response function related to terahertz frequency and crystal thickness, the detection spectrum response of ZnTe electro-optic crystal to terahertz pulse was calculated theoretically and the relation between terahertz spectrum response bandwidth and crystal thickness was gotten qualitatively. From the calculation result, some detection blind spots were found such as 5.3 THz and 6.2 THz which come from the lattice resonances of ZnTe crystal with corresponding frequency terahertz wave. With a large aperture terahertz photoconductive antenna and a 1 kHz pulse repetition frequency terahertz time-domain spectroscopy experiment system, six optimum matching angles between the polarization direction of terahertz pulse and the crystal axis direction of <110> type ZnTe crystal were obtained experimentally by differential detection technology. The curve and empirical formula of the change of the maximum terahertz electric field with the angle between the crystal axis and terahertz wave polarization direction were given, which will be beneficial to in-depth understanding of the phenomenon and the effective improvement of detection sensitivity in practice.