In case of chlorine doping, a CdTe-base compound semiconductor single crystal used for an electro-optic element has a crystal which is set to chlorine concentration ranging from 0.1 ppmwt to 5.0 ppmwt and has no precipitation having diameter of 2 μm or above. In case of chlorine doping, an indium doping, a CdTe-base compound semiconductor single crystal used for an electro-optic element has a crystal which is obtained from a CdTe material melt, to which indium is doped at concentration ranging from 0.01 ppmwt to 1.0 ppmwt, according to a liquid phase epitaxial growth method and has a solidification ratio of 0.9 or below.