It has been proposed that antigenic evolution of hemagglutinin 1 (HA1) for H3N2 human influenza A virus was punctuated. In the population genetic analysis, however, it was controversial whether positive selection operated on HA1 in a punctuated manner for the branches of the phylogenetic tree where transitions to new antigenic clusters occurred (C branches), or continuously. In the molecular evolutionary analysis, positive selection was detected for the trunk (T) branches but the relationship between antigenic evolution and positive selection was unclear. Here molecular evolutionary analysis was conducted to examine natural selection operating on HA1 of H3N2 human influenza A virus by dividing HA1 into epitopes A-E and other sites, as well as dividing the phylogenetic tree into the C branches overlapping with the T branches (C-T branches), those not overlapping with the T branches (C-NT branches), the T branches not overlapping with the C branches (NC-T branches), and other branches (NC-NT branches). Positive selection was detected for C, T, and NC-T branches, whereas evolution for the NC-NT branches appeared to be mainly neutral. Positive selection appeared to have operated throughout the trunk, which covered the entire time period of the phylogenetic tree, suggesting that positive selection operated continuously on HA1 during evolution of H3N2 human influenza A virus.