The natural plant dietary polyphenols 1,2,3,4,6-O-Pentagalloylglucose (PGG) and proanthocyanidin (PAC) have potent antioxidant activity and a variety of pharmacological activities, including antiviral activity. In this study, we examined the inhibitory effect of PGG and PAC on SARS-CoV-2 virus infection, and elucidated its mode of action. PGG and PAC have dose-dependent inhibitory activity against SARS-CoV-2 infection in Vero cells. PGG has a lower IC50 (15.02 ± 0.75 μM) than PAC (25.90 ± 0.81 μM), suggesting that PGG has better inhibitory activity against SARS-CoV-2 than PAC. The PGG and PAC inhibit similar Mpro activities in a protease activity assay, with IC50 values of 25–26 μM. The effects of PGG and PAC on the activity of the other essential SARS-CoV-2 viral protein, RdRp, were analyzed using a cell-based activity assay system. The activity of RdRp is inhibited by PGG and PAC, and PGG has a lower IC50 (5.098 ± 1.089 μM) than PAC (21.022 ± 1.202 μM), which is consistent with their inhibitory capacity of SARS-CoV-2 infection. PGG and PAC also inhibit infection by SARS-CoV and MERS-CoV. These data indicate that PGG and PAC may be candidate broad-spectrum anticoronaviral therapeutic agents, simultaneously targeting the Mpro and RdRp proteins of SARS-CoV-2.