It is to define the resistivity and the contained amount of impurities of a CdTe system compound semiconductor single crystal and to provide a CdTe system compound semiconductor single crystal which is useful as a substrate for optical devices such as an infrared sensor and the like. In a CdTe system compound semiconductor single crystal for an optical device, a Group 1 (1A) element is included in a range of 5.times.10.sup.14 to 6.times.10.sup.15 cm.sup.-3 in the crystal, a total amount of a Group 13 (3B) element and a Group 17 (7B) element included in the crystal is less than 2.times.10.sup.15 cm.sup.-3 and less than a total amount of the Group 1 (1A) element, and resistivity of the crystal is in a range of 10 to 104 .OMEGA.cm.