The severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) has caused a worldwide pandemic. The identification of effective antiviral drugs remains an urgent medical need. In this context, here we report 17 new 1,4-benzopyrone derivatives, which have been designed, synthesized, and characterized for their ability to block the RNA-dependent RNA polymerase (RdRp) enzyme, a promising target for antiviral drug discovery. This compound series represents a good starting point for developing non-nucleoside inhibitors of RdRp. Compounds 4, 5, and 8 were the most promising drug-like candidates with good potency in inhibiting RdRp, improved in vitro pharmacokinetics compared to the initial hits, and no cytotoxicity effects on normal cell (HEK-293). Compound 8 (ARN25592) stands out as the most promising inhibitor. Our results indicate that this new chemical class of 1,4-benzopyrone derivatives deserves further exploration towards novel and potent antiviral drugs for the treatment of SARS-CoV-2 and potentially other viruses.