SARS-CoV-2 RNA-dependent RNA polymerase (RdRp) protein is the target for the antiviral drug Remdesivir (RDV). With RDV clinical trials on COVID-19 patients showing a reduced hospitalisation time. During the spread of the virus, the RdRp has developed several mutations, with the most frequent being A97V and P323L. The current study sought to investigate whether A97V and P323L mutations influence the binding of RDV to the RdRp of SARS-CoV-2 compared to wild-type (WT). The interaction of RDV with WT-, A97V-, and P323L-RdRp were measured using molecular dynamic (MD) simulations, and the free binding energies were extracted. Results showed that RDV that bound to WT- and A97V-RdRp had a similar dynamic motion and internal residue fluctuations, whereas RDV interaction with P323L-RdRp exhibited a tighter molecular conformation, with a high internal motion near the active site. This was further corroborated with RDV showing a higher binding affinity to P323L-RdRp (-24.1 kcal/mol) in comparison to WT-RdRp (-17.3 kcal/mol). This study provides insight into the potential significance of administering RDV to patients carrying the SARS-CoV-2 P323L-RdRp mutation, which may have a more favourable chance of alleviating the SARS-CoV-2 illness in comparison to WT-RdRp carriers, thereby suggesting further scientific consensus for the usage of Remdesivir as clinical candidate against COVID-19.