The present invention relates to [1] an aqueous composition for ink-jet printing containing a carbodiimide compound, a vinyl polymer and water, in which the vinyl polymer is dispersed in the aqueous composition in the form of polymer particles formed by partially neutralizing carboxy groups of the vinyl polymer with a basic compound having a boiling point of not higher than 130° C.; [2] an ink set for ink-jet printing containing an aqueous composition a containing a carbodiimide compound and water, and an aqueous composition b containing a vinyl polymer; and [3] an ink-jet printing method including the step 1 of ejecting a carbodiimide compound, a pigment, a vinyl polymer and water by an ink-jetting method to print characters or images, and the step 2 of subjecting the resulting printed characters or images to heat treatment at a temperature of 50 to 200° C. According to the aqueous composition of the present invention, it is possible to obtain a printed material that is excellent in rub fatness.