Inhibition of CPSF30 function by the effector domain of influenza A virus of non-structural protein 1 (NS1A) protein plays a critical role in the suppression of host key antiviral response. The CPSF30-binding site of NS1A appears to be a very attractive target for the development of new drugs against influenza A virus. In this study, structure-based molecular docking was utilized to screen more than 30,000 compounds from a Traditional Chinese Medicine (TCM) database. Four drug-like compounds were selected as potential inhibitors for the CPSF30-binding site of NS1A. Docking conformation analysis results showed that these potential inhibitors could bind to the CPSF30-binding site with strong hydrophobic interactions and weak hydrogen bonds. Molecular dynamics simulations and MM-PBSA calculations suggested that two of the inhibitors, compounds 32056 and 31674, could stably bind to the CPSF30-binding site with high binding free energy. These two compounds could be modified to achieve higher binding affinity, so that they may be used as potential leads in the development of new anti-influenza drugs.