G-quadruplex (G4) with stacked G-tetrads structure is able to bind hemin (iron (III)-protoporphyrin IX) to form a unique type of DNAzyme/RNAzyme with peroxidase-mimicking activity, which has been widely employed in multidisciplinary fields. However, its further applications are hampered by its relatively weak activity compared with protein enzymes. Herein, we report a unique intramolecular enhancement effect of the adjacent adenine (EnEAA) at 3′ end of G4 core sequences that significantly improves the activity of G4 DNAzymes. Through detailed investigations of the EnEAA, the added 3′ adenine was proved to accelerate the compound I formation in catalytic cycle and thus improve the G4 DNAzyme activity. EnEAA was found to be highly dependent on the unprotonated state of the N1 of adenine, substantiating that adenine might function as a general acid–base catalyst. Further adenine analogs analysis supported that both N1 and exocyclic 6-amino groups in adenine played key role in the catalysis. Moreover, we proved that EnEAA was generally applicable for various parallel G-quadruplex structures and even G4 RNAzyme. Our studies implied that adenine might act analogously as the distal histidine in protein peroxidases, which shed light on the fundamental understanding and rational design of G4 DNAzyme/RNAzyme catalysts with enhanced functions.