A color conversion apparatus is for converting an input point defined in a three-dimensional first color space into an output point defined in a three-dimensional second color space. The color conversion apparatus includes: a position identifying unit; a first conversion unit; a second conversion unit; and an output point identifying unit. The position identifying unit identifies a two-dimensional position for the input point, the two-dimensional position being defined on a specific plane passing through a first white point, a first black point and the input point, the first white point and the first black point being defined in the first color space. The first conversion unit converts the input point into an intermediate point that is defined in a device-independent color space. The second conversion unit converts the intermediate point into a temporary output point that is defined in the three-dimensional second color space. The output point identifying unit identifies, in the second color space, an output point, whose position defined on a plane that passes through a second white point, a second black point and the temporary output point corresponds to the two-dimensional position identified by the position identifying unit, the second white point and the second black point being defined in the second color space.