The genus Laurencia, a category of marine red algae, is well recognized for producing a large variety of natural products (NPs) that are both chemically intriguing and structurally distinct. The aim of this research was to identify NPs with potential anti-SARS-CoV-2 activity. The crystals of the proteins RdRp and nsp15 were obtained from the RCSB protein database. About 300 NPs were discovered using the PubChem, ChemSpider, and CMNPD databases. The program Autodock Vina was used to conduct the molecular docking procedure once the proteins and ligands were prepared. Before running MD simulations using the CABS-flex 2.0 website, binding affinity assessments and interactions between amino acids were carefully reviewed. Only nine NPs were shortlisted to be examined further. Bromophycolide R, S, and bromophycoic acid C show the tendency to inhibit RdRp by β-hairpin motif binding at the N-terminal known as Active site 2 (AS2), whereas the other four NPs, bromophycolide E, H, P, and thyrsenol A, may effectively inhibit RdRp through interactions via C-terminal, also known as the Active site 1 (AS1). For the enzyme nsp15, bromophycoic B, C, and floridoside showed plausible interactions. In conclusion, out of nine, seven candidates shortlisted for RdRp exhibited strong interactions with the key residues in the AS1 and AS2 regions. Bromophycoic acid C may work as a dual inhibitor due to its favorable interactions with the nsp15 protein and RdRp’s N-terminal, with affinities of −8.5 and −8.2 kcal/mol, respectively.