Influenza viruses pose a significant threat to the public and are a burden on global health systems1,2. Each year, influenza vaccines must be rapidly produced to match circulating viruses, a process constrained by dated technology and vulnerable to unexpected strains emerging from humans and animal reservoirs. Here we use knowledge of protein structure to design self-assembling nanoparticles that elicit broader and more potent immunity than traditional influenza vaccines. The viral haemagglutinin was genetically fused to ferritin, a protein that naturally forms nanoparticles composed of 24 identical polypeptides3. Haemagglutinin was inserted at the interface of adjacent subunits so that it spontaneously assembled and generated eight trimeric viral spikes on its surface. Immunization with this influenza nanoparticle vaccine elicited haemagglutination inhibition antibody titres more than tenfold higher than those from the licensed inactivated vaccine. Furthermore, it elicited neutralizing antibodies to two highly conserved vulnerable haemagglutinin structures that are targets of universal vaccines: the stem4,5and the receptor binding site on the head6,7. Antibodies elicited by a 1999 haemagglutinin–nanoparticle vaccine neutralized H1N1 viruses from 1934 to 2007 and protected ferrets from an unmatched 2007 H1N1 virus challenge. This structure-based, self-assembling synthetic nanoparticle vaccine improves the potency and breadth of influenza virus immunity, and it provides a foundation for building broader vaccine protection against emerging influenza viruses and other pathogens.