Currently, no approved treatment for COVID-19 exists. However, phenolic compounds exhibit antiviral activity. This study aimed to evaluate the activities of polyphenolic compounds (gallic acid, quercetin, caffeine, resveratrol, naringenin, benzoic acid, oleuropein, and ellagic acid) as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) RNA-dependent RNA polymerase (PDB ID 6M71) inhibitors. Molecular docking simulations of these polyphenols were performed using Autodock 4.0 and Chimera 1.8.1. Druglikeness and pharmacokinetic properties were calculated using the SWISSADME prediction website. Remdesivir and ribavirin were used for comparison. The docking analysis results, ranked by the binding energy value (ΔG) of the tested ligands toward SARS-CoV-2 polymerase, were remdesivir > gallic acid > quercetin > caffeine > ribavirin > resveratrol > naringenin > benzoic acid > oleuropein > ellagic acid, with binding energies of −8.51, −7.55, −7.17, −6.10, −6.01, −5.79, −5.69, −5.54, −4.94, and −4.59 kcal/mol, respectively. All tested polyphenols were predicted to form hydrogen bonds with one or two of the nucleotide triphosphate (NTP) entry channels at ARG 553, ARG 555, or LYS 545, except caffeine and oleuropein, which may influence the entry of substrate and divalent cations into the central active site cavity, thereby inhibiting enzyme activity. It appears promising that gallic acid and quercetin exhibited higher binding affinity than ribavirin toward the SARS-CoV-2 polymerase and expressed good druglikeness and pharmacokinetic properties. Additionally, resveratrol, naringenin, and benzoic and ellagic acids exhibited some efficacy as potential polymerase inhibitors. Further research is required to investigate the potential uses of these polyphenols in the treatment of COVID-19.