Heme binds to a parallel-stranded G-quadruplex DNA to form a peroxidase-mimicking heme-DNAzyme. An interpolyelectrolyte complex between the heme-DNAzyme and a cationic copolymer possessing protonated amino groups was characterized and the peroxidase activity of the complex was evaluated to elucidate the effect of the polymer on the catalytic activity of the heme-DNAzyme. We found that the catalytic activity of the heme-DNAzyme is enhanced through the formation of the interpolyelectrolyte complex due to the general acid catalysis of protonated amino groups of the polymer, enhancing the formation of the iron(IV)oxo porphyrin π-cation radical intermediate known as Compound I. This finding indicates that the polymer with protonated amino groups can act as a cocatalyst for the heme-DNAzyme in the oxidation catalysis. We also found that the enhancement of the activity of the heme-DNAzyme by the polymer depends on the local heme environment such as the negative charge density in the proximity of the heme and substrate accessibility to the heme. These findings provide novel insights as to molecular design of the heme-DNAzyme for enhancing its catalytic activity.