Starting from December 2019, coronavirus disease 2019 (COVID-19) has emerged as a once-in-a-century pandemic with deadly consequences, which urgently calls for new treatments, cures and supporting apparatuses. Remdesivir was reported by World Health Organization (WHO) as the most promising drug currently available for the treatment of COVID-19. Here, we use molecular dynamics simulations and free energy perturbation methods to study the inhibition mechanism of remdesivir to its target SARS-CoV-2 virus RNA-dependent RNA polymerase (RdRp). In the absence of a crystal structure of the SARS-CoV-2 RdRp, we first construct the homology model of this polymerase based on a previously available structure of SARS-CoV NSP12 RdRp (with a sequence identify of 95.8%). We then build the putative binding mode by aligning the remdesivir + RdRp complex to the ATP bound poliovirus RdRp. The putative binding structure is further optimized with molecular dynamics simulations and demonstrated to be stable, indicating a reasonable binding mode for remdesivir. The relative binding free energy of remdesivir is calculated to be -8.28 ± 0.65 kcal/mol, much stronger than the natural substrate ATP (-4.14 ± 0.89 kcal/mol) which is needed for the polymerization. The ~800-fold improvement in the K_d from remdesivir over ATP indicates an effective replacement of APT in blocking of the RdRp binding pocket. Key residues D618, S549 and R555 are found to be the contributors to the binding affinity of remdesivir. These findings demonstrate that remdesivir can potentially act as a SARS-CoV-2 RNA-chain terminator, effectively stopping its RNA reproduction, with key residues also identified for future lead optimization and/or drug resistance studies.