To provide an aqueous dispersion of an acid-modified ethylene-based polymer having fine and good dispersion stability along with high adhesive strength, through conducting an acid-modifying reaction for the high acid modification rate of the corresponding ethylene-based polymer while suppressing its gelatinization by bringing its decline in the rate of MFR (melt flow rate) variation to 30% or less.

A method for producing the acid-modified ethylene-based polymer is provided, comprising: compounding 100 pts.mass of the ethylene-based polymer (A) described below, 1-40 pts.mass of at least the monomer (B) described below and 0.01-2 pts.mass of a mercaptan (C) followed by grafting the polymer using 0.05-0.5 pt.mass of an organic peroxide (D). The polymer (A) is an ethylene-based polymer having at least ethylene-derived structural units; and the monomer (B) is a monomer having at least one unsaturated group and at least one functional group selected from carboxy, acid anhydride and carboxylic ester groups.