The evolutionary speed and the consequent immune escape of H3N2 influenza A virus make it an interesting evolutionary system. Charged amino acid residues are often significant contributors to the free energy of binding for protein-protein interactions, including antibody-antigen binding and ligand-receptor binding. We used Markov chain theory and maximum likelihood estimation to model the evolution of the number of charged amino acids on the dominant epitope in the hemagglutinin protein of circulating H3N2 virus strains. The number of charged amino acids increased in the dominant epitope B of the H3N2 virus since introduction in humans in 1968. When epitope A became dominant in 1989, the number of charged amino acids increased in epitope A and decreased in epitope B. Interestingly, the number of charged residues in the dominant epitope of the dominant circulating strain is never fewer than that in the vaccine strain. We propose these results indicate selective pressure for charged amino acids that increase the affinity of the virus epitope for water and decrease the affinity for host antibodies. The standard PAM model of generic protein evolution is unable to capture these trends. The reduced alphabet Markov model (RAMM) model we introduce captures the increased selective pressure for charged amino acids in the dominant epitope of hemagglutinin of H3N2 influenza (R (2) > 0.98 between 1968 and 1988). The RAMM model calibrated to historical H3N2 influenza virus evolution in humans fit well to the H3N2/Wyoming virus evolution data from Guinea pig animal model studies.