We present the investigation of a high-level control of the inter- and intramolecular H-bonding in the topology-controlled poly(glycidoxy carbonyl benzoic acid)s (PGCs) (i.e., linear, hyperbranched, and branched cyclic structures). The PGCs were successfully prepared by introducing the aromatic carboxylic acids in the corresponding polyglycidols (PGs). The obtained 3 types of PGCs were demonstrated the high-level interplay between the inter- and intramolecular H-bonding in polymer chains by exhibiting the pH-dependent self-association in the solution state and the strong adhesion in the bulk state with high transparency. Interestingly, the dramatically enhanced adhesive property by 2.6-fold was demonstrated by simple mixing of branched cyclic PGC and topology-controlled PGs to promote the cooperative H-bonding between polymer chains. We anticipate the new class of cooperative H-bonding between topology-controlled polymers contribute to the development of advanced adhesive.