There are provided an ink jet printing apparatus and a color conversion processing device that can prevent the generation of offset and blocking and can stably jet ink. A first LUT in which a total amount of ink after conversion is large overall and a second LUT in which a total amount of ink after conversion is small overall are prepared as a look-up table (LUT) that is used in color conversion processing. A LUT to be used is selected according to the number of printed mediums. The first LUT is selected in a case in which the number of printed mediums is smaller than a threshold value, and the second LUT is selected in a case in which the number of printed mediums is equal to or larger than a threshold value.