The size dependent optical band gap of the less-toxic ternary I-III-VI2 chalcopyrite-type semiconductor quantum dots (QDs), CuInS2, CuInSe2, CuGaS2, CuGaSe2, AgInSe2, AgGaS2, and AgGaSe2, were evaluated using the finite-depth-well effective mass approximation calculation. From the comparison of the calculation result with the experimental values for the CuInS2 case, it was shown that the calculation was highly valid to predict the size dependent optical gap of the ternary semiconductor QDs. The optical band gap of the above seven I-III-VI2 QDs covers a wide wavelength range from the near-infrared to ultraviolet. It has been shown that the I-III-VI2 semiconductor QDs have a significant potential as alternatives to the highly toxic cadmium-containing II-VI semiconductor QDs and they are applicable to the wide range of light emitting devices and solar cells.