Understanding the nature and origin of the asteroid population in Earth's vicinity (near-Earth asteroids, and its subset of potentially hazardous asteroids) is a matter of both scientific interest and practical importance. It is generally expected that the compositions of the asteroids that are most likely to hit Earth should reflect those of the most common meteorites. Here we report that most near-Earth asteroids (including the potentially hazardous subset) have spectral properties quantitatively similar to the class of meteorites known as LL chondrites. The prominent Flora family in the inner part of the asteroid belt shares the same spectral properties, suggesting that it is a dominant source of near-Earth asteroids. The observed similarity of near-Earth asteroids to LL chondrites is, however, surprising, as this meteorite class is relatively rare ( approximately 8 per cent of all meteorite falls). One possible explanation is the role of a size-dependent process, such as the Yarkovsky effect, in transporting material from the main belt.