To provide a polymer which selectively adsorbs an acidic water-soluble target substance, a polymer which has a specific recognition site for an acidic water-soluble target substance, a production process thereof, and an acidic water-soluble target substance-adsorbing agentA polymer which selectively adsorbs at least one kind of an acidic water-soluble target substance, in which the polymer has a cross-linked structure formed through a two-step reaction including a Michael addition reaction of a polymer having an amino group and/or imino group with an unsaturated carbonyl cross-linker, and a subsequent radical polymerization.