Finding new neuraminidase (N) inhibitors to improve anti-influenza treatment is necessary because of the high mutation rates of N protein. Over 3,000 flavones/flavonols and their synthesized products from the COCONUT database were performed in silico docking screening with N1-H274Y-oseltamivir protein (PDB ID: 3CL0). Several derivatives containing nitrogen heterocyclic groups or aromatic rings showed higher anti-neuraminidase potential than that of laninamivir. Especially, the linker groups between the flavone aglycone and nitrogen heterocyclic group created the interactions with the triad of arginine residues Arg118-Arg292-Arg371, which suggested these compounds could become bifunctional inhibitors against the influenza virus strains at the sialic acid binding site and the adjacent 430-cavity position through triad of arginine residues binding. ADMET indicators and the synthesis design strategy of the most suitable compound, ethyl 4-{2-[(5-hydroxy-4-oxo-2-phenyl-4H-chromen-7-yl)oxy]acetyl}piperazine-1-carboxylate, were also successfully predicted and it could be a concerned candidate for further wet-lab synthesis, in vivo and clinical study.