Paper for ink jet printing has to obtain optimal printing runnability, printability, and printing quality. Therefore, it must have some specific properties that ensure optimal drying time, mechanical stability of a print, and its light and water resistance. The paper surface should enable the printing ink to be dried as fast as possible. The aim of the applied research was to determine how an ink jet color print on paper changes with time immediately after printing, and how long it takes for the color print to stabilize. Color differences ΔE*_ab were measured that appeared on print after a certain amount of time with regards to values attained immediately after printing. The influence of paper on colorimetric properties and optical density of a print was analyzed by measuring some structural, surface, and sorption properties. The values attained show that the paper surface should enable wetting and ink penetration in paper structure. The biggest changes in colorimetric properties of the print became visible during 1 h after printing; however, color print finally stabilizes only after 96 h. Research results confirmed the importance of paper sorption properties for obtaining high-quality ink jet color prints.