This invention provides a graft modified polypropylene polymer which does not contain halogens, is excellent in certain properties such as solubility and can add good adhesiveness and coating ability to crystalline propylene polymer base materials, and a composition containing the same; and in particular, it provides a propylene polymer which contains a propylene polymer main chain having a stereo-block structure containing an isotactic block and a side chain containing a carboxylic acid group, an acid anhydride group or a carboxylic acid ester group, wherein when it is dissolved in toluene to a concentration of 10% by weight at 25.degree. C., the insoluble matter is 1% by weight or less based on the total polymer, and a composition containing the same.