Novel dual-targeted, bifunctional anti-influenza drugs formed by conjugation with anti-inflammatory agents are disclosed. Exemplary drugs according to the invention include caffeic acid (CA)-bearing zanamivir (ZA) conjugates ZA-7-CA (1), ZA-7-CA-amide (7) and ZA-7-Nap (43) for simultaneous inhibition of influenza virus neuraminidase and suppression of proinflammatory cytokines. Synthetic methods for preparation of these enhanced anti-influenza conjugate drugs are provided. The synthetic bifunctional ZA conjugates act synergistically towards protection of mice lethally infected by H1N1 or H5N1 influenza viruses. The efficacy of ZA-7-CA, ZA-7-CA-amide and ZA-7-Nap conjugates is much greater than the combination therapy of ZA with anti-inflammatory agents.