Starting from late 2019, the 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. Recently, because of its positive results in clinical trials, remdesivir was approved by Food and Drug Administration to treat COVID-19 through Emergency Use Authorization. Here, we used 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). We first constructed 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 built a putative pre-insertion binding structure by aligning the remdesivir + RdRp complex to the ATP bound poliovirus RdRp without the RNA template. The putative binding structure was further optimized with molecular dynamics simulations. The resulting stable pre-insertion state of remdesivir appeared to form hydrogen bonds with the RNA template when aligned with the newly solved cryo-EM structure of SARS-CoV-2 RdRp. The relative binding free energy between remdesivir and ATP was calculated to be -2.80 ± 0.84 kcal/mol, where remdesivir bound much stronger to SARS-CoV-2 RdRp than the natural substrate ATP. The ~100-fold improvement in the Kd from remdesivir over ATP indicates an effective replacement of ATP in blocking of the RdRp pre-insertion site. Key residues D618, S549 and R555 are found to be the contributors to the binding affinity of remdesivir. These findings suggest that remdesivir can potentially act as a SARS-CoV-2 RNA-chain terminator, effectively stopping its RNA replication, with key residues also identified for future lead optimization and/or drug resistance studies.