The rapid spread of the COVID-19 outbreak is now a global threat with over a million diagnosed cases and more than 70 thousand deaths. Specific treatments and effective drugs regarding such disease are in urgent need. To contribute to the drug discovery against COVID-19, we performed computational study to understand the inhibition mechanism of the COVID-19 3c-like protease, and search for possible drug candidates from approved or experimental drugs through drug repurposing screening against the DrugBank database. Two novel computational methods were applied in this study. We applied the “Consecutive Histogram Monte Carlo” (CHMC) sampling method for understanding the inhibition mechanism from studying the 2-D binding free energy landscape. We also applied the “Movable Type” (MT) free energy method for the lead compound screening by evaluating the binding free energies of the COVID-19 3c-like protease – inhibitor complexes. Lead compounds from the DrugBank database were first filtered using ligand similarity comparison to 19 published SARS 3c-like protease inhibitors. 70 selected compounds were then evaluated for protein-ligand binding affinities using the MT free energy method. 4 drug candidates with strong binding affinities and reasonable protein-ligand binding modes were selected from this study, i.e. Enalkiren (DB03395), Rupintrivir (DB05102), Saralasin (DB06763) and TRV-120027 (DB12199).