The present invention relates to [1] an aqueous composition for ink-jet printing, containing a carbodiimide compound, a polyester resin and water; [2] a ink set for ink-jet printing containing an aqueous composition a containing a carbodiimide compound and water, and an aqueous composition b containing a polyester resin; [3] an ink set for ink-jet printing, containing the aforementioned aqueous composition for ink-jet printing and a water-based ink containing a colorant; and [4] an ink-jet printing method including the step 1 of ejecting a carbodiimide compound, a polyester resin, a colorant and water onto a surface of a printing medium by an ink-jetting method to print characters or images thereon; 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.