Antiviral drug therapy against SARS-CoV-2 is not yet established and posing a serious global health issue. Remdesivir is the first antiviral compound approved by the US FDA for the SARS-CoV-2 treatment for emergency use, targeting RNA-dependent RNA polymerase (RdRp) enzyme. In this work, we have examined the action of remdesivir and other two ligands screened from the library of nucleotide analogues using docking and molecular dynamics (MD) simulation studies. The MD simulations have been performed for all the ligand-bound RdRp complexes for the 30 ns time scale. This is one of the earlier reports to perform the MD simulations studies using the SARS-CoV-2 RdRp crystal structure (PDB ID 7BTF). The MD trajectories were analyzed and Molecular Mechanics Poisson-Boltzmann Surface Area (MM-PBSA) calculations were performed to calculate the binding free energy. The binding energy data reveal that compound-17 (-59.6 kcal/mol) binds more strongly as compared to compound-8 (-46.3 kcal/mol) and remdesivir (-29.7 kcal/mol) with RdRp. The detailed analysis of trajectories shows that the remdesivir binds in the catalytic site and forms a hydrogen bond with the catalytic residues from 0 to 0.46 ns. Compound-8 binds in the catalytic site but does not form direct hydrogen bonds with catalytic residues. Compound-17 showed the formation of hydrogen bonds with catalytic residues throughout the simulation process. The MD simulation results such as hydrogen bonding, the center of mass distance analysis, snapshots at a different time interval, and binding energy suggest that compound-17 binds strongly with RdRp of SARS-CoV-2 and has the potential to develop as a new antiviral against COVID-19. Further, the frontier molecular orbital analysis and molecular electrostatic potential (MESP) iso-surface analysis using DFT calculations shed light on the superior binding of compound-17 with RdRp compared to remdesivir and compound-8. The computed as well as the experimentally reported pharmacokinetics and toxicity parameters of compound-17 is encouraging and therefore can be one of the potential candidates for the treatment of COVID-19.