Currently, the new coronavirus disease 2019 (COVID-19) is a global pandemic without any well calibrated treatment. To inactivate the SARS-CoV-2 virus that causes COVID-19, the main protease (Mpro) that performs key biological functions in the virus has been the focus of extensive studies. With the fast-response experimental efforts, the crystal structures of Mpro of the SARS-CoV-2 virus have just become available recently. Herein, we theoretically investigated the binding mechanism between the Mpro's pocket and various marketed drug molecules being tested in clinics to fight COVID-19 that show promising outcomes. Combining all existing experiment results with our computational ones, we revealed an important ligand-binding mechanism for the Mpro that the binding stability of a ligand inside the Mpro pocket can be significantly improved if the partial ligand occupies the so-called "anchor" site of the Mpro. Along with the high-potent drugs/molecules (such as nelfinavir and curcumin) revealed in this study, the newly discovered binding mechanism paves the way for further optimizations and designs of Mpro's inhibitors with a high binding affinity.