Supramolecular polymeric adhesives inspired by nature have been strongly pursued by scientists, since they possess strong but dynamic reversible adhesive behaviors concurrently. Optimizing the adhesive and cohesive properties is of vital importance for the fabrication of strong supramolecular polymeric adhesives, but common strategies often strengthen one property at the expense of another. Herein, counterion exchange of nucleobase-containing polyelectrolyte adhesives was utilized to boost the interfacial adhesion without compromising the intermolecular cohesion, achieving high adhesion strengths. By employing the cationic polyelectrolyte poly(3-acrylamidopropyltrimethylammonium chloride), the slightly enhanced intermolecular cohesion of the polyelectrolyte with hydrophobic sulfonates is capable of enhancing the adhesion strength. Intriguingly, by introducing bioinspired complementary nucleobases within adhesives, the loss of interfacial adhesion was observed for adhesives containing high supramolecular hydrogen-bonding crosslinking densities. By optimizing the cohesive and adhesive properties of nucleobase-containing polyelectrolyte adhesives using sulfonates with suitable chain lengths, 60 to 250 times improvement of adhesion strengths can be attained over that of initial supramolecular polymeric adhesives. Additionally, nucleobase-containing supramolecular polymeric adhesives tolerate different external conditions, maintaining robust adhesion strengths. This work offers us an efficient and feasible way to optimize the cohesive and adhesive properties for constructing robust and tunable supramolecular adhesives.