Rapid antigenic evolution in the influenza A virus hemagglutinin precludes effective vaccination with existing vaccines. To understand this phenomenon, we passaged virus in mice immunized with influenza vaccine. Neutralizing antibodies selected mutants with single-amino acid hemagglutinin substitutions that increased virus binding to cell surface glycan receptors. Passaging these high-avidity binding mutants in naïve mice, but not immune mice, selected for additional hemagglutinin substitutions that decreased cellular receptor binding avidity. Analyzing a panel of monoclonal antibody hemagglutinin escape mutants revealed a positive correlation between receptor binding avidity and escape from polyclonal antibodies. We propose that in response to variation in neutralizing antibody pressure between individuals, influenza A virus evolves by adjusting receptor binding avidity via amino acid substitutions throughout the hemagglutinin globular domain, many of which simultaneously alter antigenicity.