Coronavirus disease 2019 is one of the global health problems. Herein, a highly sensitive electrochemical biosensor has been designed to detect the RNA-dependent RNA polymerase (RdRP) of the severe acute respiratory syndrome coronavirus-2 (SARS-CoV-2) (SARS-CoV-2 RdRP). Herein, the surface-initiated reversible-addition−fragmentation-chain-transfer polymerization was used to amplify the electrochemical signal. To do that, the thiol-terminated peptide nucleic acid (PNA) probes were first immobilized on the surface of a screen-printed electrode modified with reduced graphene oxide-gold nanocomposite and then the fixed concentration of the SARS-CoV-2 RdRP was added to the electrode surface to interact with PNA probes. Subsequently, the Zr 4+ ions were added to interact with the phosphate groups of the SARS-CoV-2 RdRP. It allowed us to polymerase the ferrocenylmethyl methacrylate (FcMMA) and 4-cyano-4-(phenylcarbonothioylthio)-pentanoic acid on the SARS-CoV-2 RdRP chain. Since the poly-FcMMA has an electrochemical signal, the response of the PNA-based sensor to SARS-CoV-2 RdRP was increased in the range of 5–500 aM. The limit of detection was calculated to be 0.8 aM which is lower than the previous sensor for SARS-CoV-2 RdRP detection. The proposed PNA-based sensor showed high selectivity to the SARS-CoV-2 RdRP in the presence of the gene fragments of influenza A and Middle East respiratory syndrome coronavirus.