Since December 2019, novel coronavirus disease 2019 (COVID-19) pandemic has caused tremendous economic loss and serious health problems worldwide. In this study, we investigated 14 natural compounds isolated from Amphimedon sp. via a molecular docking study, to examine their ability to act as anti-COVID-19 agents. Moreover, the pharmacokinetic properties of the most promising compounds were studied. The docking study showed that virtually screened compounds were effective against the new coronavirus via dual inhibition of SARS-CoV-2 RdRp and the 3CL main protease. In particular, nakinadine B (1), 20-hepacosenoic acid (11) and amphimedoside C (12) were the most promising compounds, as they demonstrated good interactions with the pockets of both enzymes. Based on the analysis of the molecular docking results, compounds 1 and 12 were selected for molecular dynamics simulation studies. Our results showed Amphimedon sp. to be a rich source for anti-COVID-19 metabolites.