We report on the generation of terahertz (THz) radiation via optical rectification and the detection using electro-optic sampling in ZnTe crystal by the pump-probe technique. The pulsewidth of the observed THz radiation is about 0.2 ps, resulting in the wideband THz spectra with a spectral sensitivity beyond 4 THz and the full width at half-maximum of about 2.4 THz. The Jones matrix method has been employed successfully for the calculation of the THz radiation. We study the effects of the optical pulse wavelength, pulsewidth and the ZnTe crystal axis on the generation of THz radiation in the ZnTe crystal. The dependence of the polarization-modulation on the THz detection has also been investigated both experimentally and theoretically by changing the polarization of the probe light.