The present invention relates to a method for producing a modified propylene-based polymer containing modifying a propylene-based polymer by a radical initiator and an organic acid, a modified propylene-based polymer obtained by the method, and an adhesive composition containing the modified propylene-based polymer. The propylene-based polymer is a propylene homopolymer satisfying the conditions of (a) mmmm=20 to 60 mol %, (b) [rrrr/(1-mmmm)].ltoreq.0.1, (c) rmrm>2.5 mol %, (d) mmxrr/(mr).sup.2.ltoreq.2.0, and (e) the weight ratio (W25) of components eluted at 25.degree. C. or lower in a temperature programmed chromatography is 20 to 100% by weight, or a propylene copolymer satisfying the condition of (h) the stereoregularity index (P) obtained by .sup.13C-NMR measurement is 55 to 90 mol %.The modified propylene-based polymer of the invention can make a polyolefin, etc. more adhesive, stronger, or flexible, to be useful for a high-adhesive sealant or an polyolefin with increased compatibility to an inorganic filler, etc., particularly as a resin for a hot-melt adhesive.