During 2016–2017, the H7N2 feline influenza virus infected more than 500 cats in animal shelters in New York, USA. A veterinarian who had treated the cats became infected with this feline virus and showed mild respiratory symptoms. This suggests that the H7N2 feline influenza virus may evolve into a novel pandemic virus with a high pathogenicity and transmissibility as a result of mutations in humans. In this study, to gain insight into the molecular basis of the transmission of the feline virus to humans, we selected mutant viruses with enhanced growth in human respiratory A549 cells via successive passages of the virus and found almost all mutations to be in the envelope glycoproteins, such as hemagglutinin (HA) and neuraminidase (NA). The reverse genetics approach revealed that the HA mutations, HA1-H16Q, HA2-I47T, or HA2-Y119H, in the stalk region can lead to a high growth of mutant viruses in A549 cells, possibly by changing the pH threshold for membrane fusion. Furthermore, NA mutation, I28S/L, or three-amino-acid deletion in the transmembrane region can enhance viral growth in A549 cells, possibly by changing the HA–NA functional balance. These findings suggest that the H7N2 feline influenza virus has the potential to become a human pathogen by adapting to human respiratory cells, owing to the synergistic biological effect of the mutations in its envelope glycoproteins.