A carboxylic acid polymer containing a carboxylic group and having at least one kind of bond selected from the group consisting of an amino bond, an ether bond, and a thioether bond in a side chain is prepared by polymerizing a monomer component containing a carboxylic acid monomer represented by General Formula (3): ##STR1## where Y.sub.4 is a hydrogen atom, an allyl group, or a --(CHR.sub.4).sub.c --W.sub.2 --(CHR.sub.5).sub.d --COOR.sub.6 group, each of R.sub.1, R.sub.2, R.sub.3, R.sub.4, R.sub.5, and R.sub.6, independent of the others, is either a hydrogen atom or an alkyl group of a carbon number from 1 to 6, each of W.sub.1 and W.sub.2, independent of the other, is either an --NH-- group, an --S-- group, or an --O-- group, and each of a, b, c, and d, independent of the others, is an integer from 0 to 6. The carboxylic acid polymer has a superior metal-scavenging ability (chelating ability) and can be suitably used, for example, as a chelating agent.