The physical chemistry of iron at inner-core conditions is key to understanding the evolution and habitability of Earth-like planets. Based on full first-principles simulations, we report cooperative diffusion along the longitudinally fast〈111〉directions of body-centred cubic (bcc) iron in temperature ranges of 2000-4000 K below the melting curve and pressures up to 3 TPa. The diffusion is due to low energy barriers in the corresponding direction and accompanied by mechanical and dynamic stability of bcc iron. With the assistance of the diffusion, bcc iron demonstrates strong elastic anisotropy and variations with temperature and pressure, which is consistent with several seismological signatures of the Earth’s inner core, particularly the positive correlation between P wave velocity and attenuation. This finding also has implications for nucleation and growth of the inner core and suggests the exotic state and properties of iron need to be considered in future geophysical and planetary models.