Positively charged groups that mimic arginine or lysine in a natural substrate of trypsin are necessary for drugs to inhibit the trypsin-like serine protease TMPRSS2 that is involved in the viral entry and spread of coronaviruses, including SARS-CoV-2. Based on this assumption, we identified a set of 13 approved or clinically investigational drugs with positively charged guanidinobenzoyl and/or aminidinobenzoyl groups, including the experimentally verified TMPRSS2 inhibitors Camostat and Nafamostat. Molecular docking using the C-I-TASSER-predicted TMPRSS2 catalytic domain model suggested that the guanidinobenzoyl or aminidinobenzoyl group in all the drugs could form putative salt bridge interactions with the side-chain carboxyl group of Asp435 located in the S1 pocket of TMPRSS2. Molecular dynamics simulations further revealed the high stability of the putative salt bridge interactions over long-time (100 ns) simulations. The molecular mechanics/generalized Born surface area-binding free energy assessment and per-residue energy decomposition analysis also supported the strong binding interactions between TMPRSS2 and the proposed drugs. These results suggest that the proposed compounds, in addition to Camostat and Nafamostat, could be effective TMPRSS2 inhibitors for COVID-19 treatment by occupying the S1 pocket with the hallmark positively charged groups.