A longstanding question is how influenza evolves to escape human immunity, which is polyclonal and can target many distinct epitopes on the virus. Here we map how all amino-acid mutations to influenza’s major surface protein affect viral neutralization by polyclonal human sera. The serum of some individuals is so focused that it selects single mutations that reduce viral neutralization by over an order of magnitude. However, different viral mutations escape the sera of different individuals. This individual-to-individual variation in viral escape mutations is not present among ferrets, which are frequently used as a model in influenza studies. Our results show how different single mutations help influenza escape the immunity of different members of the human population, a phenomenon that could shape viral evolution and disease susceptibility.