Provided are a water dispersion for ink-jet printing, wherein it is a water dispersion of water-insoluble graft polymer particles containing a colorant; the above graft polymer contains a principal chain having a constitutional unit derived from a vinyl base monomer and a side chain which is derived from a macromer containing an aromatic ring and having a polymerizable functional group at one end; both of the Log P values of the above principal chain and the above side chain are positive; and a difference between both falls in a specific range, and a water-based ink containing the same. The above water-based ink is excellent in a discharge stability, a storage stability, a heat stability and a water resistance.